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:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
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:
[tex]\begin{gathered} m=\frac{25.60-22.20}{13-11} \\ \\ m=\frac{3.4}{2} \\ \\ m=1.7 \end{gathered}[/tex]
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
