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 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 take $(0,2)$ and $(2,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1 = 2,x_2 = 2,y_2 = 0$ into the formula:
$m=\frac{0 - 2}{2 - 0}=\frac{-2}{2}=- 1$

Step4: Write the equation

Substitute $m=-1$ and $b = 2$ into $y=mx + b$.
We get $y=-x + 2$

Answer:

$y=-x + 2$