Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify 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 ($b$)

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,-2)$, so $b=-2$.

Step3: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line. We can use the points $(0, - 2)$ and $(1,0)$ (we can also use other points like $(2,2)$ etc.).
Using $(x_1,y_1)=(0,-2)$ and $(x_2,y_2)=(1,0)$:
$m=\frac{0 - (-2)}{1 - 0}=\frac{0 + 2}{1}=2$

Step4: Write the equation

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

Answer:

$y = 2x - 2$