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Week 2

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Wednesday

Wednesday - Learn & Practice: Understanding Intercepts

I can find and interpret x- and y-intercepts.

Short Lesson

Intercepts Tell Where a Graph Crosses an Axis

At a y-intercept, x=0. At an x-intercept, y=0. The meaning depends on the variables, units, and context.

Guided Examples

Set One Variable Equal to Zero

Example 1

Find both intercepts of 2x+3y=12.

Use one zero at a time.

Step-by-step solution:

  1. x=0: 2(0)+3y=12 Set x equal to zero for the y-intercept.
Example 2

You have $20 and spend $2 each day.

The model is M=-2d+20. What does the x-intercept mean?

Step-by-step solution:

  1. M=0 At the x-intercept, the output equals zero.

Wednesday Practice

Find and Interpret Intercepts

For both-intercept questions, include both points in your answer.

Problem 1

Find the x- and y-intercepts of y=3x-6.

Example format: (0,-6), (2,0)

Problem 2

Find the x- and y-intercepts of 2x+4y=8.

Example format: (0,2), (4,0)

Problem 3

A table shows the relationship below. Find the y-intercept and predict the x-intercept.

Relationship Table
xy
010
18
26

Example format: (0,10), (5,0)

Problem 4

A line passes through (0,-2) and (3,0). Identify both intercepts.

Example format: (0,-2), (3,0)

Problem 5

A bank account begins with $20, and $4 is spent each day. What are the y- and x-intercepts?

Example format: (0,20), (5,0)

Problem 6

Find both intercepts of y=-x+5.

Example format: (0,5), (5,0)

Wednesday Mistake Analysis

Diagnose the Mistake First

Choose the best diagnosis. Then reveal the full analysis.

Given: 2x+4y=8

Student says: "The y-intercept is 8."

What is the mistake?

Given: y=3x-9

Student wants: the x-intercept and sets x=0.

What went wrong?

Model: V=-5t+100

Student says: "The x-intercept always means the situation is finished."

What is the best diagnosis?

Wednesday Reflection

How do you decide whether an x-intercept is meaningful?

End of Wednesday

Choose Where to Go Next