Question

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

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0, - 3)$, so $b=-3$.

Step3: Calculate the slope ($m$)

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

Step4: Write the equation

Substitute $m=\frac{3}{2}$ and $b = - 3$ into $y=mx + b$:
$y=\frac{3}{2}x-3$

Answer:

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