Algebra · Algebra 1 · Big Ideas Math · Ron Larson

Video solutions

• Real-World Application: Linear Modeling
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  A plant's height is measured over time. On day 8, the plant is 12 cm tall. On day 20, the plant is 26 cm tall. Write an equation in point-slope form to model the plant's height $h$ as a function of days $d$. Then convert…

• Finding Slope-Intercept Form from Two Points
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  Question: A line passes through the points 2 comma 5 and 6 comma 17. Write the equation of the line in slope-intercept form, y equals m x plus b. Show all steps to find the slope and y-intercept. Finding Slope-Intercept…

• Graphing and Interpreting Slope-Intercept Form
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  Question: The equation y equals negative 2 x plus 10 represents a linear function. Part a: Identify the slope and y-intercept. Part b: Graph the line on a coordinate plane, clearly marking the y-intercept and at least tw…

• Writing Equations from Real-World Scenarios
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  Question: A swimming pool is being drained. It starts with 8,000 gallons of water and drains at a constant rate of 250 gallons per hour. Write an equation in slope-intercept form that represents the amount of water, y in…

• Finding Linear Equation from Point and Slope
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  Question: A line passes through the point 3 comma 7 and has a slope of 2. Write the equation of the line in point-slope form, then convert it to slope-intercept form. Finding Linear Equation from Point and Slope This l…

• Writing Equation from Two Points
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 4-

  Question: Two points on a line are negative 2 comma 5 and 4 comma negative 1. Find the slope of the line, write the equation in point-slope form using one of the points, and then express it in slope-intercept form. Writ…

• Making an Input-Output Table & Graphing a Linear Function
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Complete the input-output table for the function y equals 2x minus 3 using the input values x equals negative 2, negative 1, 0, 1, and 2. Then plot the ordered pairs on a coordinate plane and describe whether t…

• Finding the Slope Between Two Points on a Graph
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Find the slope of the line passing through each pair of points. Then describe the slope as positive, negative, zero, or undefined. Part a: the points 1 comma 3 and 4 comma 9. Part b: the points negative 2 comma…

• Real-World Linear Function: Writing & Interpreting a Graph
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A service charges a flat setup fee of 40 dollars plus 12 dollars per hour. Part a: Write a linear function that represents the total cost C in dollars as a function of hours h. Part b: Identify the slope and y-…

• Plotting Points and Identifying Quadrants on the Coordinate Plane
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Plot and label each point on a coordinate plane. Then identify the quadrant or axis where each point is located. Part a: A at 3 comma 5. Part b: B at negative 4 comma 2. Part c: C at negative 1 comma negative 6…

• Graphing Linear Functions in Slope-Intercept Form
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Graph each linear function by identifying the slope and y-intercept. Label at least two points on each graph. Part a: y equals three-fourths x plus 1. Part b: y equals negative 2x plus 1. Part c: y equals x min…

• Determining Whether a Relation Is a Function
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A shop tracks the number of items sold each hour during opening hours. The data is shown in the following table. Time in hours after opening, paired with Items Sold: hour 1 sold 24 items, hour 2 sold 35 items, …

• Identifying Functions from Sets, Graphs, and Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Three relations are shown. Relation A is the set of ordered pairs: negative one comma four, zero comma two, one comma zero, two comma two, and three comma four. Relation B is a graph showing points at negative …

• Evaluating and Analyzing a Linear Function
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Given the function f of x equals negative 2x plus 7, where x represents the number of video game rentals per day: Part a — Evaluate f of 3 and explain what it means in context. Part b — If the store can process…

• Finding the Linear Function from Two Points on a Graph
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A parking garage charges a base fee plus an hourly rate. After 2 hours, the total charge is 16 dollars. After 5 hours, the total charge is 31 dollars. Write a linear function f of h that represents the total co…

• Interpreting Linear Functions in Real-World Context
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A phone company's monthly bill is modeled by the function c of m equals 35 plus 0.12 times m, where m is the number of minutes used and c of m is the total cost in dollars. Part a: Identify the y-intercept and …

• Writing and Comparing Linear Function Rules
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Two fitness centers offer membership plans. Center A charges 40 dollars per month with no enrollment fee. Center B charges 25 dollars per month with a 90 dollar enrollment fee. Part a: Write linear functions f …

• Finding Function Values from an Equation
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Let f of x equal negative 2x plus 7. Find f of negative 3, f of 0, and f of 5. Then explain what each result represents as a point on the graph of f. Finding Function Values from an Equation This lesson cover…

• Writing and Using a Function Model
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A cell phone plan charges a 15-dollar monthly fee plus 8 cents per minute of talk time. Write a function C of m that gives the total monthly cost in dollars for m minutes of talk time. Then find C of 200 and C …

• Solving Equations Using Function Notation
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Let g of x equal 3x minus 4. For what value of x does g of x equal 11? Verify your solution and describe the corresponding point on the graph of g. Solving Equations Using Function Notation This lesson demons…

• Converting Standard Form to Graph
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A bakery's revenue equation is given in standard form: 3x plus 4y equals 24, where x represents the number of loaves sold and y represents the number of pastries sold. Convert this equation to slope-intercept f…

• Standard Form with Negative Coefficients
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Graph the equation 5x minus 2y equals 10 using the standard form method. Find both intercepts algebraically, plot them on a graph, and draw the line. Then determine three points that lie on this line and verify…

• Finding Slope and Y-Intercept from an Equation
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Write the equation y equals negative 3 x plus 7 in slope-intercept form and identify the slope and y-intercept. Then describe what each value tells you about the graph. Finding Slope and Y-Intercept from an Eq…

• Graphing Using Slope-Intercept Form
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Graph the equation y equals two-fifths x minus 4 by first plotting the y-intercept, then using the slope to find at least two more points. Verify that all points satisfy the equation. Graphing Using Slope-Inte…

• Converting Standard Form to Slope-Intercept Form and Graphing
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Convert the equation 3x plus 2y equals 12 to slope-intercept form. Then identify the slope and y-intercept, and sketch the graph using these values. Converting Standard Form to Slope-Intercept Form and Graphin…

• Direct Variation: Recipe Scaling Problem
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A recipe for trail mix requires 3 cups of nuts for every 2 cups of dried fruit. Write a direct variation equation relating the cups of nuts, n, to the cups of dried fruit, d. Then determine how many cups of nut…

• Direct Variation: Hourly Earnings Model
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: A worker earns 14 dollars and 50 cents per hour. Write a direct variation equation where earnings, e, vary directly with hours worked, h. If the worker needs to earn 232 dollars, how many hours must they work? …

• Direct Variation: Distance-Speed Relationship
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Two cars travel at constant speeds. Car A travels 156 miles in 3 hours, and Car B travels 117 miles in 2.25 hours. Write a direct variation equation for each car relating distance d to time t. Which car is fast…

• Vertical Shift of a Linear Function
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: The graph of f of x equals 2x is shifted up 5 units to create a new function g of x. Write the equation for g of x and identify the y-intercept of the new function. Then describe how the slope is affected by th…

• Horizontal Shift and Reflection Combined
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: Start with the parent function f of x equals x. First shift the graph 3 units to the right, then reflect it across the x-axis to create function h of x. Write the equation for h of x. Verify your equation by te…

• Multiple Transformations and Function Composition
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 3-

  Question: The linear function p of x equals negative 3x plus 2 undergoes the following transformations in order: first, shift left 4 units; second, stretch vertically by a factor of 2; third, shift down 6 units. Write th…

• Multi-Step Inequality Word Problem
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: A club is selling candles for a fundraiser. Each candle sells for 8 dollars. The club already has 35 dollars donated. They need to raise at least 200 dollars total to fund their event. Write and solve a multi-s…

• Writing and Graphing Linear Inequalities
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: A roller coaster requires riders to be at least 48 inches tall. Part a: Write an inequality that represents the height h, in inches, a person must be to ride. Part b: Graph the inequality on a number line. Part…

• Solving One-Step Linear Inequalities
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve each inequality and graph the solution on a number line. Part a: 4x is greater than 28. Part b: n divided by 3 is less than or equal to negative 5. Part c: 12 is less than 6t. Also explain why the inequal…

• Solving and Graphing Linear Inequalities in Context
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: A savings account currently holds 45 dollars. The goal is to have more than 120 dollars saved before making a purchase. Write and solve an inequality to find the minimum additional amount d, in dollars, that mu…

• Solving and Graphing Linear Inequalities
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve each inequality and graph the solution on a number line. Part a: 3x plus 7 is greater than 19. Part b: 5 minus 2n is less than or equal to 13. Part c: 4 times the quantity y minus 3 is greater than or equ…

• Solving Linear Inequalities Using Addition and Subtraction
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve each inequality and graph the solution on a number line. Part a: x plus 9 is less than 14. Part b: m minus 6 is greater than or equal to negative 2. Part c: 7 plus y is less than or equal to 3. For part c…

• Solving Compound Inequalities
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve each compound inequality and graph the solution on a number line. Part a: negative 4 is less than 2x plus 6, which is less than or equal to 14. Part b: 3 is less than or equal to 5 minus n, which is less …

• Reading and Writing Inequalities from Number-Line Graphs
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Write the inequality shown by each graph and describe the solution in words. Part (a): a number line with an open circle at negative 3 and shading to the left. Part (b): a number line with a closed circle at 5 …

• Solving a One-Step Linear Inequality | Add or Subtract
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve the inequality and graph the solution on a number line. x minus 7 is greater than negative 3. Write the solution in inequality notation and interval notation. Solving a One-Step Linear Inequality | Add o…

• Solving a One-Step Linear Inequality | Multiply or Divide
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve the inequality and graph the solution on a number line. Negative four x is greater than or equal to twenty. Write the solution in inequality notation and interval notation. Explain what happens to the ine…

• Solving a Multi-Step Linear Inequality
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve the inequality, graph the solution, and write the solution in interval notation. 3x plus 8 is less than or equal to 2x minus 4. Check your solution by substituting a value from the solution set back into …

• Solving a Compound Inequality | AND
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: Solve the compound inequality and graph the solution on a number line: negative 2 is less than 3x minus 5, which is less than or equal to 10. Write the solution in inequality notation and interval notation. Sta…

• Solving a Real-World Linear Inequality | Word Problem
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 2-

  Question: A fundraiser sells candles for 6 dollars each. The club has already raised 45 dollars from donations. They need to raise MORE THAN 150 dollars in total. Part a: Write an inequality to represent the situation, w…

• Solving One-Step Equations | Multiplication & Division
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and check your solutions. Part a: 6 times m equals negative 54. Part b: n divided by 8 equals negative 3. Part c: negative 5 times p equals 35. Solving One-Step Equations | Multiplication &…

• Solving One-Step Equations | Addition & Subtraction
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and check the solution. Part a: x plus 14 equals 31. Part b: y minus 9 equals negative 4. Part c: negative 7 plus z equals 22. Solving One-Step Equations | Addition & Subtraction This less…

• Solving Multi-Step Equations | Two Operations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and check your solutions. Part a: 3x plus 7 equals 28. Part b: 4y minus 11 equals 13. Part c: negative 2z plus 5 equals negative 9. Solving Multi-Step Equations | Two Operations This lesso…

• Solving Multi-Step Equations with the Distributive Property
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and check your solution. Part a: 2 times the quantity 3x minus 4, equals 16. Part b: negative 3 times the quantity y plus 6, equals 9. Part c: 5 times the quantity 2w minus 1, plus 8, equals…

• Rewriting Literal Equations | Solving for a Variable
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation for the indicated variable. Part a: P equals 2l plus 2w, solve for w. Part b: A equals one-half times b times h, solve for b. Part c: V equals l times w times h, solve for l. Part d: C equal…

• Absolute Value Equations | Basic Cases
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and check both solutions in the original equation. Part a: the absolute value of x equals 11. Part b: the absolute value of the quantity m minus 4 equals 7. Part c: the absolute value of the…

• Absolute Value Equations | Multi-Step & No Solution
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation, or state if there is no solution. Check all solutions. Part a: 2 times the absolute value of x plus 3, minus 5, equals 9. Part b: the absolute value of 4y minus 8, plus 6, equals 2. Part c:…

• Special Solutions: No Solution and Identity Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation and classify the result. Part a: 4 times the quantity x plus 2, equals 4x minus 6. Part b: 3 times the quantity 2y minus 1, equals 6y minus 3. Part c: 5z plus 10 equals 5 times the quantity …

• Writing and Solving One-Variable Equations from Word Problems
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Set up and solve an equation for each scenario. Part a: A phone plan charges a 25-dollar flat fee plus 10 cents per text message. If the bill is 47 dollars, how many texts were sent? Part b: Two hikers start at…

• Solving Linear Equations with Variables on Both Sides
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve each equation. Part a: 5x plus 3 equals 2x plus 18. Part b: 7 minus 4y equals 2y minus 11. Part c: 6 times the quantity w minus 2, equals 3w plus 6. Identify the solution, or state if it has no solution o…

• Solving One-Step Multiplication & Division Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: 7x equals 91. Show each step and verify your solution. Solving One-Step Multiplication & Division Equations This lesson demonstrates how to solve a one-step linear equation in which the va…

• Solving a Literal Equation for a Specific Variable
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: The formula for the perimeter of a rectangle is P equals 2 times l plus 2 times w. Part a: Solve the formula for l, the length. Part b: Use the result to find the length of a rectangle with a perimeter of 54 ce…

• Solving Equations with Fractions
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: three-fourths x plus 2 equals one-half x plus 7. Eliminate fractions using the least common denominator, then solve. Verify your answer. Solving Equations with Fractions This lesson teache…

• Solving Multi-Step Equations with Like Terms
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: 5x plus 3x minus 10 equals 38. Combine like terms first, then isolate the variable. Show all steps and check your solution. Solving Multi-Step Equations with Like Terms This lesson walks t…

• Solving Equations Using the Distributive Property
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: 4 times the quantity 2x minus 3, equals 28. Apply the distributive property first, then solve the resulting two-step equation. Check your answer. Solving Equations Using the Distributive Pr…

• Solving Absolute Value Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: the absolute value of 2x minus 6 equals 10. Write two separate cases, solve each, and check both solutions in the original equation. Solving Absolute Value Equations This lesson covers how…

• Writing & Solving a Linear Equation from a Word Problem
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: A movie streaming service charges a flat monthly fee of 8 dollars plus 3 dollars per premium movie rented. If a customer's bill for one month is 26 dollars, write and solve an equation to find how many premium …

• Solving Equations with Variables on Both Sides
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: 6x plus 5 equals 2x plus 21. Collect variable terms on one side and constants on the other. Show each step and verify the solution. Solving Equations with Variables on Both Sides This less…

• Solving Two-Step Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: 3x minus 8 equals 16. Identify the two operations applied to x and undo them in reverse order. Verify your answer. Solving Two-Step Equations This lesson teaches students how to solve a tw…

• Solving One-Step Addition & Subtraction Equations
  Algebra · Algebra 1 · Big Ideas Math · Ron Larson · Chapter 1

  Question: Solve the equation: x plus 14 equals 29. Show each step and check your answer by substituting back into the original equation. Solving One-Step Addition & Subtraction Equations This lesson demonstrates how to…

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