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 400 pounds of cans?

Answer 1

p starts with 100 lbs Rufus already collected. The question is asking as he collects 25 lbs each week, what is the equation that describes the total pounds of aluminum collected.

p = 100 + something.

What is that something? Rufus is collecting 25 lbs each week. After 2 week, he will have collected 25+25 = 50 which also depends on the number of weeks. in other word he will have collected 25 * w lbs after w weeks later.

then

p = 100 + 25 * w = 25 * w + 100

What does the slope and y-intercept represent?

The slope is the rate at which Rufus collects the cans as the week passes. What do you think y-intercept of 100 represent based on the text?

How long will it take Rufus to collect 400 pounds of cans?

400 lbs is the total pounds or p.

400 = 25 w +100

Solve for w

300 = 25 w

w= 12