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 and point - slope form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. We know that $m = 6$ and the point $(x_1,y_1)=(-4,-20)$.

Step2: Substitute into point - slope form

Substitute $m = 6$, $x_1=-4$ and $y_1 = - 20$ into the point - slope form:
$y-(-20)=6(x - (-4))$
Simplify the left - hand side and the right - hand side:
$y + 20=6(x + 4)$

Step3: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, where $a = 6$, $b=x$ and $c = 4$, we get:
$y+20=6x+24$

Step4: Solve for y (get slope - intercept form)

Subtract 20 from both sides of the equation:
$y=6x+24 - 20$
Simplify the right - hand side:
$y=6x + 4$

Answer:

$y = 6x+4$