Question

a line has a slope of -4 and passes through the point (-1, 10). 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 $m=-4$, so the equation becomes $y=-4x + b$.

Step2: Find the value of $b$

Substitute the point $(-1,10)$ into the equation $y=-4x + b$. We get $10=-4\times(-1)+b$.
Simplify the right - hand side: $10 = 4 + b$.
Subtract 4 from both sides to solve for $b$: $b=10 - 4=6$.

Step3: Write the final equation

Substitute $b = 6$ back into $y=-4x + b$. The equation of the line in slope - intercept form is $y=-4x+6$.

Answer:

$y=-4x + 6$