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 $(3,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-3,x_2 = 3,y_2 = 0$ into the formula:
$m=\frac{0-(-3)}{3 - 0}=\frac{3}{3}=1$

Step4: Write the equation

Substitute $m = 1$ and $b=-3$ into $y=mx + b$.
We get $y=x-3$.

Answer:

$y = x - 3$