Question

a line passes through the point (2, -6) 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 $(2,-6)$, so $x_1 = 2$ and $y_1=-6$. The slope $m=-4$.

Step3: Substitute values into the formula

Substitute $x_1 = 2$, $y_1=-6$ and $m = - 4$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y-(-6)=-4(x - 2)$, which simplifies to $y + 6=-4(x - 2)$.

Answer:

$y + 6=-4(x - 2)$