the graph shows the relationship between the weight of a box and the number of books added to the box. what…

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.

Step2: Find the y - intercept

The y - intercept is the value of $y$ when $x = 0$. From the graph, when $x=0$, $y = 2$. So $b = 2$.

Step3: Calculate the slope

Let's take two points from the graph, say $(0,2)$ and $(4,5)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 2}{4-0}=\frac{3}{4}=0.75$.

Step4: Determine the function

The function is $f(x)=0.75x + 2$.

Answer:

$f(x)=0.75x + 2$