Question

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

Explanation:

Step1: Find two points on the line

Let's take the points $(0, 2)$ and $(2,0)$.

Step2: Calculate the slope $m$

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

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,2)$, $b = 2$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m=-1$ and $b = 2$ gives $y=-x + 2$.

Answer:

$y=-x + 2$