Writing Slope-Intercept Form Practice

Question

Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. Write the equation for the total pounds, p, of aluminum cans after w weeks. What does the slope and y-intercept represent? How long will it take Rufus to collect 409 pounds of cans?

Answer 1

Hi Aubrie,

Using the variables given in your problem, the equation (in slope-intercept form) would be:

p = 25w + 100

The slope is 25 pounds/week and the y- intercept is 100 pounds.

The slope represents the unit rate or the number of pounds he collects in one week. The y intercept is 100 pounds and represents the amount he had before starting to keep track.

To find the number of weeks it would take to reach 409 pounds, you woould substitute 409 in the equation for p and solve for w. Using oppsite operations, this would be:

p= 25w + 100

409 = 25w + 100

Subtract 100 from each side of the equation:

409-100 = 25w + 100 -100

309 = 25w

Divide both sides by 25:

309/25 = 25w/25

12.36 = w

It would take 12.36 weeks

Hope this helps you!

Irene