Question

1. the graph of a function is a line that passes through the points (0, 1) and (3, 10). write an equation in the form y = mx + b for this function.

Explanation:

Step1: Identify y-intercept ($b$)

The point $(0, 1)$ is the y-intercept, so $b = 1$.

Step2: Calculate slope ($m$)

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(3,10)$
$m=\frac{10-1}{3-0}=\frac{9}{3}=3$

Step3: Substitute $m$ and $b$ into $y=mx+b$

Substitute $m=3$ and $b=1$ into the slope-intercept form.

Answer:

$y=3x+1$