Question

a line has a slope of 6 and passes through the point (-2, -16). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

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 $m = 6$, and the line passes through the point $(x,y)=(-2,-16)$. Substitute these values into the equation:
$-16=6\times(-2)+b$

Step2: Solve for $b$

First, calculate $6\times(-2)$: $6\times(-2)=-12$. So the equation becomes:
$-16=-12 + b$
To solve for $b$, add 12 to both sides of the equation:
$b=-16 + 12=-4$

Step3: Write the equation

Now that we know $m = 6$ and $b=-4$, substitute these values into the slope - intercept form $y=mx + b$:
$y = 6x-4$

Answer:

$y = 6x-4$