Question

a line has a slope of 4 and passes through the point (-1, -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 $m = 4$, so the equation is $y=4x + b$.

Step2: Substitute the point into the equation

The line passes through the point $(1,-4)$. Substitute $x = 1$ and $y=-4$ into $y = 4x + b$. We get $-4=4\times1 + b$.

Step3: Solve for $b$

Simplify the right - hand side of the equation: $-4 = 4 + b$. Subtract 4 from both sides: $b=-4 - 4=-8$.

Answer:

$y = 4x-8$