Question

a line passes through the point (-2, 7) and has a slope of -4. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify values of $x_1$, $y_1$ and $m$

We are given that the line passes through the point $(-2,7)$, so $x_1=-2$ and $y_1 = 7$. The slope $m=-4$.

Step3: Substitute values into the formula

Substitute $x_1=-2$, $y_1 = 7$ and $m=-4$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 7=-4(x - (-2))$, which simplifies to $y - 7=-4(x + 2)$.

Answer:

$y - 7=-4(x + 2)$