Writing an equation

Question

A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 100 units. For each additional $2000 spent, an additional 20 units are sold.

I understand that per each $100 being spent, an additional unit is sold, and I understand that the y-intercept or the initial number of units sold is 100. My first equation I tried to write was y=100x+100, but I keep getting marked incorrect. Can anyone help me understand what I'm writing incorrectly?

Answer 1

That's not how you do it.

Since this is linear and you have the y-intercept, let's use the slope-intercept form of a linear equation:

y = mx + b

Let x = amount of money spent

y = number of items sold.

your b (y-intercept) is 100

coordinate form is (0,100)

y= mx + 100

The problem says "For each additional $2000 spent, an additional 20 units are sold."

That means

when x = 2000,

y = 100+20 =120

coordinate form is (2000,120)

So plugin those values to the equation to solve for slope m:

120 = m(2000) + 100

120-100 = m(2000)

20 = m(2000)

20/2000 = m

Therefore:

m = 1/100

Your final equation is :

y = (1/100)x +100

------

Let's check:

If x = $2000, will we get y = 120 units?

y= (1/100)(2000) + 100

y = 20 +100

y = 120. Yes it is correct.