Question

a line has a slope of 6 and passes through the point (-4, -20). 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 $m = 6$, so the equation is $y=6x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(-4,-20)$. Substitute $x=-4$ and $y = - 20$ into $y=6x + b$:
$$-20=6\times(-4)+b$$

Step3: Solve for $b$

First, calculate $6\times(-4)=-24$. Then the equation becomes:
$$-20=-24 + b$$
Add 24 to both sides of the equation:
$$b=-20 + 24=4$$

Step4: Write the final equation

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

Answer:

$y = 6x + 4$