Question

a line has a slope of 4 and passes through the point (3, 18). 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 $m = 4$, and the line passes through the point $(x,y)=(3,18)$.

Step2: Substitute values into the equation

Substitute $m = 4$, $x = 3$, and $y = 18$ into the equation $y=mx + b$. So we have $18=4\times3 + b$.

Step3: Solve for $b$

First, calculate $4\times3=12$. Then the equation becomes $18 = 12 + b$. Subtract 12 from both sides of the equation: $b=18 - 12=6$.

Step4: Write the equation

Now that we know $m = 4$ and $b = 6$, substitute these values back into the slope - intercept form $y=mx + b$. We get $y = 4x+6$.

Answer:

$y = 4x + 6$