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,

Recall that the slope-intercept equation has the form y=mx + b, where m is the slope and b is the y-intercept. Here, we're asked for an equation in terms of total p in pounds, so that's our y. First side of the equation is:

p=

Similarly, we'll replace x with w for weeks. Now, we need m, our slope. Rufus wants to collect 25 pounds of trash per week. Slope, in this case, is pounds of trash collected multiplied by time. Therefore:

m=25 and we have:

p=25w + b

Now, we need b, our y-intercept. Rufus began with 100 pounds of trash. This is his starting point, so on a graph, that would be where the line hits the y-axis, our y-intercept. So, the final equation is:

p=25w + 100

Now, we want to know how long it takes Rufus to collect 409 pounds, so substitute that value in for p in the equation and solve for w:

409=25w + 100

Subtract 100 from both sides:

309=25w

Divide both sides by 25:

w=12.36 weeks, or just over 3 months.

I hope this helps. Good luck.