Question

a line has a slope of $-\frac{2}{5}$ and passes through the point $(-1, 0)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We know that $m =-\frac{2}{5}$ and the point is $(-1,0)$, so $x_1=-1$ and $y_1 = 0$.
Substitute these values into the point - slope form: $y-0=-\frac{2}{5}(x - (-1))$, which simplifies to $y=-\frac{2}{5}(x + 1)$.

Step2: Convert to slope - intercept form

Slope - intercept form is $y=mx + b$. We expand the right - hand side of the equation from Step 1.
Using the distributive property $a(b + c)=ab+ac$, where $a =-\frac{2}{5}$, $b=x$, and $c = 1$, we get $y=-\frac{2}{5}x-\frac{2}{5}(1)$.
So $y=-\frac{2}{5}x-\frac{2}{5}$.

Answer:

$y =-\frac{2}{5}x-\frac{2}{5}$