Question

a line has a slope of - 3 and passes through the point (-7, 1). 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 $m=-3$, so the equation becomes $y=-3x + b$.

Step2: Substitute the point into the equation

Substitute $x=-7$ and $y = 1$ into $y=-3x + b$. We get $1=-3\times(-7)+b$.

Step3: Solve for $b$

First, calculate $-3\times(-7)=21$. Then the equation $1 = 21 + b$ can be solved for $b$ by subtracting 21 from both sides. So $b=1 - 21=-20$.

Step4: Write the final equation

Substitute $b = - 20$ back into $y=-3x + b$. The equation of the line in slope - intercept form is $y=-3x-20$.

Answer:

$y=-3x - 20$