Question

write the equation of this line 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.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0, - 5)$, so $b=-5$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take the y - intercept $(0, - 5)$ and another point, say $(8, - 1)$ (from the graph). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-5,x_2 = 8,y_2=-1$ into the formula:
$m=\frac{-1-(-5)}{8 - 0}=\frac{-1 + 5}{8}=\frac{4}{8}=\frac{1}{2}$

Step4: Write the equation

Substitute $m=\frac{1}{2}$ and $b = - 5$ into the slope - intercept form $y=mx + b$.
We get $y=\frac{1}{2}x-5$

Answer:

$y=\frac{1}{2}x - 5$