Question

a line has a slope of 3 and passes through the point (-2, -10). 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 $m = 3$, so the equation becomes $y=3x + b$.

Step2: Substitute the point into the equation

Substitute $x=-2$ and $y = - 10$ into $y = 3x + b$. We get $-10=3\times(-2)+b$.

Step3: Solve for $b$

First, simplify the right - hand side: $3\times(-2)=-6$. So the equation is $-10=-6 + b$. Add 6 to both sides of the equation: $-10 + 6=b$, which gives $b=-4$.

Step4: Write the final equation

Substitute $b = - 4$ back into $y=3x + b$. The equation of the line in slope - intercept form is $y = 3x-4$.

Answer:

$y = 3x-4$