Calculate Slope of Linear Function: Points A(0,-10) and B(4,1)

To solve this problem, we need to calculate the slope of the line passing through the points $A(0, -10)$ and $B(4, 1)$.

The formula for the slope $m$ of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Given the points $A(0, -10)$ and $B(4, 1)$, we identify:

• $x_1 = 0, y_1 = -10$
• $x_2 = 4, y_2 = 1$

Substituting these values into the slope formula, we have:

$m = \frac{1 - (-10)}{4 - 0}$

This simplifies to:

$m = \frac{1 + 10}{4} = \frac{11}{4}$

The fraction $\frac{11}{4}$ can be converted to a mixed number:

$\frac{11}{4} = 2\frac{3}{4}$

Therefore, the slope of the graph is $\bm{2\frac{3}{4}}$.