Question

Can you write an equation for the function in slope intercept form?

Answer 1

Given the table of the function:

Tank size (gal) Total cost

(x) f(x)

11 22.20

13 25.60

19 35.80

To write an equation for the function in slope intercept form, use the slope intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, use the formula:

`m=(y2-y1)/(x2-x1)`

Take two points on the table:

(x1, y1) ==> (11, 22.20)

(x2, y2) ==> (13, 25.60)

Input the values into the slope formula and find the slope.

We have:

`\begin{gathered} m=(25.60-22.20)/(13-11) \\ \\ m=(3.4)/(2) \\ \\ m=1.7 \end{gathered}`

The slope is 1.7

Substitute 1.7 for m in the slope intercept form:

y = 1.7x + b

To solve for b, substitute 11 for x and 22.30 for y:

y = 1.7x + b

22.20 = 1.7(11) + b

22.20 = 18.7 + b

Substitue 18.7 from both sides:

22.20 - 18.7 = 18.7 - 18.7 + b

3.5 = b

b = 3.5

Thus, the slope intercept form of the function is:

y = 1.7x + 3.5

ANSWER:

y = 1.7x + 3.5