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Free Fall 2026 NC Math 1 Weekly Support

Week 3

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Wednesday

Wednesday - Build the Skill: Parallel & Perpendicular Lines

I can determine whether lines are parallel or perpendicular based on their equations.

Short Lesson

Slope Tells the Relationship Between Lines

Parallel Lines

Parallel lines have the same slope: m1=m2.

Perpendicular Lines

Perpendicular lines have opposite reciprocal slopes.

Defined Slopes

For slopes that are defined, m1*m2=-1.

Guided Examples

Compare or Create Slopes

Example 1

Write an equation for a line perpendicular to y=-2x+5 that passes through (0,0).

Use the opposite reciprocal slope.

Step-by-step solution:

  1. m=-2 Identify the original slope.
Example 2

Determine whether y=3x+1 and y=-(1/3)x+5 are parallel, perpendicular, or neither.

Identify and compare the slopes.

Step-by-step solution:

  1. m1=3 The first line has slope 3.

Wednesday Practice

Use Slope Properties

Compare the slopes first, then decide what that comparison tells you.

Problem 1

Are y=4x-2 and y=4x+7 parallel, perpendicular, or neither?

Choose one

Problem 2

Find the slope of a line perpendicular to y=-(1/5)x+3.

Problem 3

Write an equation for a line parallel to y=-3x+1 that passes through (0,4).

Problem 4

What is the product of the slopes of two perpendicular lines when both slopes are defined?

Problem 5

Write an equation for a line perpendicular to y=(1/2)x-3 that passes through (0,2).

Wednesday Mistake Analysis

Diagnose the Mistake First

Choose the best diagnosis. Then reveal the full analysis.

Given: 5, 8, 11, ...

Student writes: an=5+3n

What is the mistake?

Given: perpendicular slope to m=4

Student answers: m=-4

What is the mistake?

Given: 2, 6, 10, ...

Student writes: an=an-1*3

What is the mistake?

Wednesday Reflection

Which strategy helps you most when working with slopes?

End of Wednesday

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