Question

write the equation of this line in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

Let's take the points $(0, - 2)$ and $(4,0)$.

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 $(x_2,y_2)=(4,0)$ gives $m=\frac{0 - (-2)}{4-0}=\frac{2}{4}=\frac{1}{2}$.

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 $m=\frac{1}{2}$ and $b = - 2$ gives $y=\frac{1}{2}x-2$.

Answer:

$y=\frac{1}{2}x - 2$