I'm having trouble with this.

Question

a lawn care company charges $25 per month of lawn maintenance plus an initial service fee. the total cost for service fee and 8 months of maintenance is $165. write the point slope form of an equation to find the total cost y for any number of months x

Answer 1

We have a linear equation here, and we're asked to find the answer using the point-slope formula:

y - y₁ = m(x - x₁)

y₁ = 165 (the total cost is $165)

m = 25 (the company charges $25 a month)

x₁ = 8 (the cost is after 8 months)

 

That leaves us with the following:

y - 165 = 25(x - 8)

Distribute:

y - 165 = 25x - 200

add 165:

y = 25x - 35

 

That seems to be off, because that would imply that the company paid the homeowner $35. Let's see how it looks from the slope-intercept form:

y = mx + b

165 = 25 * 8 + b

165 = 200 + b

-35 = b

 

So I don't know if there's a typo above, or if the question itself was written wrong, but as it currently stands, the company is covering the first month plus change.