Question

a line has a slope of 1/3 and passes through the point (3, - 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. Given $m=\frac{1}{3}$ and the point $(x = 3,y=-20)$.

Step2: Substitute values into the equation

Substitute $x = 3$, $y=-20$ and $m=\frac{1}{3}$ into $y=mx + b$. We get $-20=\frac{1}{3}\times3 + b$.

Step3: Solve for $b$

First, simplify the right - hand side: $\frac{1}{3}\times3=1$. So the equation becomes $-20 = 1 + b$. Then subtract 1 from both sides: $b=-20 - 1=-21$.

Step4: Write the equation of the line

Substitute $m=\frac{1}{3}$ and $b = - 21$ back into $y=mx + b$. The equation is $y=\frac{1}{3}x-21$.

Answer:

$y=\frac{1}{3}x - 21$