Question

a line has a slope of -4 and passes through the point (-4, 17). 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

Substitute $x=-4$ and $y = 17$ into $y=-4x + b$. We get $17=-4\times(-4)+b$.

Step3: Solve for $b$

First, calculate $-4\times(-4)=16$. Then the equation becomes $17 = 16 + b$. Subtract 16 from both sides: $b=17 - 16=1$.

Step4: Write the final equation

Substitute $b = 1$ back into $y=-4x + b$. The equation of the line in slope - intercept form is $y=-4x + 1$.

Answer:

$y=-4x + 1$