Question

question 19 (02.04 mc) damon has $40 to spend at a baseball game. the linear function, f(x), can be used to find the number of concession - stand items he can purchase at the game. the table shown gives values of f(x) at selected values of x.

x	0	1	4	5
f(x)	40	38	32	30

find the equation that models this situation and solve for x. (1 point)
f(x)=-2x + 40; x = $20
f(x)=-2x + 40; x = 20 items
f(x)=2x + 40; x = $20
f(x)=2x + 40; x = 20 items

Explanation:

Step1: Find the slope

The slope $m$ of a linear - function $y = mx + b$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,40)$ and $(x_2,y_2)=(1,38)$. Then $m=\frac{38 - 40}{1-0}=\frac{-2}{1}=-2$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the table, when $x = 0$, $f(x)=40$, so $b = 40$.
The linear function is $f(x)=-2x + 40$.

Step3: Solve for $x$ when $f(x)=0$ (when all the money is spent)

Set $f(x)=0$, so $0=-2x + 40$. Add $2x$ to both sides: $2x=40$. Divide both sides by 2: $x = 20$ (items).

Answer:

B. $f(x)=-2x + 40;x = 20$ items