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

Answer:

$y = -2x + 7$

Explanation:

Step1: Identify two points

From the graph, we can see the line passes through $(0, 7)$ (the y - intercept) and $(3, 1)$ (we can find another point by moving 3 units right and 6 units down from $(0,7)$).

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(0,7)$ as $(x_1,y_1)$ and $(3,1)$ as $(x_2,y_2)$, we get $m=\frac{1 - 7}{3 - 0}=\frac{-6}{3}=-2$.

Step3: Write the equation

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m=-2$ and $b = 7$ (from the point $(0,7)$), so the equation is $y=-2x + 7$.