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 y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0, - 4)$, so $b=-4$.

Step3: Calculate the slope

To find the slope $m$, we can use two points on the line. Let's take two points: $(0, - 4)$ and $(4, - 5)$ (we can also use other points). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-4,x_2 = 4,y_2=-5$ into the formula:
$m=\frac{-5-(-4)}{4 - 0}=\frac{-5 + 4}{4}=\frac{-1}{4}=-\frac{1}{4}$

Step4: Write the equation

Substitute $m =-\frac{1}{4}$ and $b=-4$ into the slope - intercept form $y=mx + b$.
We get $y=-\frac{1}{4}x-4$

Answer:

$y =-\frac{1}{4}x - 4$