find the rule of the following linear function in slope - intercept form.

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(5,9)$. Then $m=\frac{9 - 1}{5-(-3)}=\frac{8}{8}=1$.

Step2: Find the y - intercept

Use the slope - intercept form $y = mx + b$ and substitute one of the points, say $(5,9)$ and $m = 1$. So $9=1\times5 + b$. Solving for $b$ gives $b=9 - 5=4$.

Step3: Write the linear function

The slope - intercept form is $y=mx + b$. Substituting $m = 1$ and $b = 4$ we get $y=x + 4$.

Answer:

$y=x + 4$