Question

a line passes through the point (-2, -1) and has a slope of -5. write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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. We know that $m=-5$, $x_1 = - 2$ and $y_1=-1$. Substitute these values into the point - slope form:
$y-(-1)=-5(x - (-2))$
Simplify the left - hand side and the right - hand side: $y + 1=-5(x + 2)$

Step2: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, where $a=-5$, $b = x$ and $c = 2$, we get:
$y+1=-5x-10$

Step3: Solve for y (slope - intercept form $y=mx + b$)

Subtract 1 from both sides of the equation:
$y=-5x-10 - 1$
Simplify the right - hand side: $y=-5x-11$

Answer:

$y = - 5x-11$