Question

a line has a slope of -7 and passes through the point (2, -2). 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 $m=-7$, so the equation becomes $y=-7x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 2,y=-2)$ into $y=-7x + b$. We get $-2=-7\times2 + b$.

Step3: Solve for $b$

First, calculate $-7\times2=-14$. The equation is $-2=-14 + b$. Add 14 to both sides: $-2+14=-14 + b+14$. So, $b = 12$.

Step4: Write the final equation

Substitute $b = 12$ back into $y=-7x + b$. The equation of the line in slope - intercept form is $y=-7x + 12$.

Answer:

$y=-7x + 12$