Question

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

Explanation:

Step1: Recall 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 line crosses the y - axis at $(0,2)$, so $b = 2$.

Step3: Calculate the slope ($m$)

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

Step4: Write the equation

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

Answer:

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