Identifying Parallel and Perpendicular Lines from Equations

Question:
Determine whether the lines 4x minus 2y equals 8, y equals 2x plus 3, and 3y equals negative 6x plus 9 are parallel, perpendicular, or neither to each other. Justify your answer by comparing slopes.

Identifying Parallel and Perpendicular Lines from Equations

This lesson teaches students how to determine whether pairs of lines are parallel, perpendicular, or neither by converting each equation into slope-intercept form and comparing slopes. Students practice rewriting standard-form and non-standard equations, then apply the rules that parallel lines share equal slopes and perpendicular lines have slopes whose product is −1.

In this lesson, you will learn to:
• Convert linear equations from standard form into slope-intercept form y = mx + b.
• Identify the slope and y-intercept of a line from its slope-intercept equation.
• Apply the parallel-slope rule (equal slopes, differen