Question

the graph shows the relationship between the amount of change given from a $10 bill and the number of bagels purchased. what function represents the amount of change given from a $10 bill, f(x), based on x, the number of bagels purchased? o f(x) = 4/3 x + 10 o f(x)= - 4/3 x + 10 o f(x) = 3/4 x + 10 o f(x)= - 3/4 x + 10

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $y=f(x)$, and the initial amount of money is $10$, so $b = 10$.

Step2: Calculate the slope

We can use two points on the line, say $(0,10)$ (when $x = 0$ bags are bought, change is $10$) and $(4,7)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 10}{4-0}=\frac{- 3}{4}$.

Step3: Write the function

Substituting $m =-\frac{3}{4}$ and $b = 10$ into $y=mx + b$, we get $f(x)=-\frac{3}{4}x + 10$.

Answer:

$f(x)=-\frac{3}{4}x + 10$