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 passes through the origin $(0,0)$, so when $x = 0$, $y=0$. So the y - intercept $b = 0$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take the points $(0,0)$ and $(1, - 3)$ (we can see from the graph that when $x = 1$, $y=-3$). The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1, - 3)$ into the formula, we get $m=\frac{-3 - 0}{1 - 0}=\frac{-3}{1}=-3$.

Step4: Write the equation

Substitute $m=-3$ and $b = 0$ into the slope - intercept form $y=mx + b$. We get $y=-3x+0$, which simplifies to $y=-3x$.

Answer:

$y = - 3x$