Question

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 ($m$)

We can use two points on the line to find the slope. Let's use the points $(0, - 2)$ and $(2,1)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-2,x_2 = 2,y_2 = 1$ into the formula:
$m=\frac{1-(-2)}{2 - 0}=\frac{1 + 2}{2}=\frac{3}{2}$

Step4: Write the equation

Substitute $m=\frac{3}{2}$ and $b = - 2$ into the slope - intercept form $y=mx + b$.
We get $y=\frac{3}{2}x-2$

Answer:

$y=\frac{3}{2}x - 2$