a line passes through the points (-4, -4) and (1, 6). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-4,-4)$ and $(x_2,y_2)=(1,6)$. Then $m=\frac{6 - (-4)}{1-(-4)}=\frac{6 + 4}{1 + 4}=\frac{10}{5}=2$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and substitute one of the points and the slope. Let's use the point $(1,6)$ and $m = 2$. So $6=2\times1 + b$. Solving for $b$ gives $b=6 - 2=4$.

Step3: Write the equation

The slope - intercept form of the line is $y=mx + b$. Substituting $m = 2$ and $b = 4$, we get $y=2x + 4$.

Answer:

$y = 2x+4$