Question

a line has a slope of $\frac{1}{3}$ and passes through the point (14, 4). 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 $m=\frac{1}{3}$, so the equation becomes $y=\frac{1}{3}x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 14,y = 4)$ into $y=\frac{1}{3}x + b$. We get $4=\frac{1}{3}\times14 + b$.

Step3: Solve for $b$

First, calculate $\frac{1}{3}\times14=\frac{14}{3}$. Then the equation is $4=\frac{14}{3}+b$. Rewrite 4 as $\frac{12}{3}$, so $\frac{12}{3}=\frac{14}{3}+b$. Subtract $\frac{14}{3}$ from both sides: $b=\frac{12}{3}-\frac{14}{3}=-\frac{2}{3}$.

Step4: Write the final equation

Substitute $b =-\frac{2}{3}$ back into $y=\frac{1}{3}x + b$. The equation of the line is $y=\frac{1}{3}x-\frac{2}{3}$.

Answer:

$y=\frac{1}{3}x-\frac{2}{3}$