Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.
y =

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

The line passes through the origin $(0,0)$, so the y - intercept $b = 0$.

Step3: Calculate the slope

We can use two points on the line, for example, $(0,0)$ and $(2,-1)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1 = 0,x_2=2,y_2=-1$ into the formula, we get $m=\frac{-1 - 0}{2 - 0}=-\frac{1}{2}$.

Step4: Write the equation

Since $m =-\frac{1}{2}$ and $b = 0$, the equation of the line in slope - intercept form is $y=-\frac{1}{2}x+0$, which simplifies to $y =-\frac{1}{2}x$.

Answer:

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