Question

a line passes through the point (-4, -8) and has a slope of 5. write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the slope $m = 5$. So we can start with the equation $y=5x + b$.

Step2: Substitute the point into the equation

We know that the line passes through the point $(-4,-8)$. Substitute $x=-4$ and $y = - 8$ into the equation $y=5x + b$:

$$
LATEXBLOCK0
$$

Step3: Solve for $b$

To solve for $b$, we add 20 to both sides of the equation:

$$
LATEXBLOCK1
$$

Step4: Write the final equation

Now that we know $m = 5$ and $b = 12$, we substitute these values back into the slope - intercept form $y=mx + b$. So the equation of the line is $y = 5x+12$.

Answer:

$y = 5x + 12$