Question

Type the correct answer in the box.

The table below represents the total cost of leasing a car at the end each month.
Month
1
3
Cost
$1,859
$2,577
$4,372
$5,808
8
12
Write an equation in slope-intercept form to represent the total cost. y. of leasing a car for x months.

Answer 1

y = 359x + 1500

((PIC INCLUDED))

Explanation:

to write an equation or function in slope intercept form (y=mx+b), first fill out the known values, in this case we got points on a plot

(1,1859)

(3,2577)

(8,4372)

and (12,5808)

to find the slope between these, lets first find the closest two points (makes it easier, but can be done with any two points along a linier graph) for this it will be the first two

now subtract the y-value of the first point from the second point

2577 - 1859 = 718

then devide that by the difference in the x-values between the two points

3 - 1 = 2

718 / 2 = 359

we can now implement the slope (m) into the equation

y = 359x + b

now that we know the slope we can find out what the y intercept (b) is, the slope indicates that as we add 1 in x value, the y value increases by 359, since this works in reverse as well, we can go to our first point, subtract 1 x value (so x = 0) and subtract m from the y value times the x value (359)

1859 - 359 = 1500

meaning that y = 1500 at x = 0, so the y intercept (b) is 1500, insert that value as follows

y = 359x + 1500

all points fall along the line plotted by this function, meaning this is the correct answer