Question

write an equation in slope - intercept form
7.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
From the graph, the y - intercept ($b$) is 2 because the line crosses the y - axis at $(0,2)$.

Step2: Calculate the slope ($m$)

We can use two points on the line. We know one point is $(0,2)$ and another point is $(3, - 2)$ (from the graph). The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(3, - 2)$. Then $m=\frac{-2 - 2}{3 - 0}=\frac{-4}{3}$? Wait, no, wait. Wait, another point: when $x = 1$, $y=0$? Wait, no, let's re - examine the graph. Wait, the line passes through $(0,2)$ and $(2,0)$? Wait, no, the point at $x = 3$ is $y=-2$? Wait, maybe I made a mistake. Let's take two clear points. The y - intercept is $(0,2)$. Then, when $x = 1$, $y = 1$? No, wait, the line goes from $(0,2)$ to $(2,0)$? Wait, no, the point at $x = 3$ is $(3,-2)$. Wait, let's calculate the slope between $(0,2)$ and $(3,-2)$. The change in $y$ is $-2 - 2=-4$, change in $x$ is $3 - 0 = 3$, so $m=\frac{-4}{3}$? No, that can't be. Wait, maybe the two points are $(0,2)$ and $(1,1)$? No, the graph: when $x = 0$, $y = 2$; when $x = 2$, $y = 0$? Wait, no, the point at $x = 3$ is $(3,-2)$. Wait, let's do it correctly. Let's take $(0,2)$ and $(2,0)$. Then $m=\frac{0 - 2}{2 - 0}=\frac{-2}{2}=-1$. Ah, that's better. Because from $(0,2)$ to $(2,0)$, the run is $2$ (from $x = 0$ to $x = 2$) and the rise is $-2$ (from $y = 2$ to $y = 0$). So $m=\frac{-2}{2}=-1$.

Step3: Write the equation

Now that we have $m=-1$ and $b = 2$, substitute into $y=mx + b$. So $y=-1x+2$ or $y=-x + 2$.

Answer:

$y=-x + 2$