Question

1. write the equation of the line shown on the grid in slope - intercept 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

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. Let's take the points $(0,0)$ and $(1, - 2)$ (we can see from the grid that when $x = 1$, $y=-2$). The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1, - 2)$ into the formula, we get $m=\frac{-2 - 0}{1 - 0}=\frac{-2}{1}=-2$.

Step4: Write the equation

Substitute $m=-2$ and $b = 0$ into the slope - intercept form $y=mx + b$. We get $y=-2x+0$, which simplifies to $y=-2x$.

Answer:

$y = - 2x$