a line has a slope of 4 and passes through the point (-1, -4). write its equation in slope - intercept 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 $m = 4$, so the equation becomes $y=4x + b$.

Step2: Substitute the point into the equation

Substitute $x=-1$ and $y = - 4$ into $y = 4x + b$. We get $-4=4\times(-1)+b$.

Step3: Solve for $b$

First, simplify the right - hand side: $4\times(-1)=-4$. So the equation is $-4=-4 + b$. Add 4 to both sides of the equation: $-4 + 4=-4 + 4 + b$, which gives $b = 0$.

Step4: Write the final equation

Substitute $b = 0$ back into $y=4x + b$. The equation of the line in slope - intercept form is $y = 4x$.

Answer:

$y = 4x$