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 two clear - cut points. Suppose the line passes through $(-8,-3)$ and $(8,-7)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(-8,-3)$ and $(x_2,y_2)=(8,-7)$ gives $m=\frac{-7-(-3)}{8 - (-8)}=\frac{-7 + 3}{8 + 8}=\frac{-4}{16}=-\frac{1}{4}$.

Step3: Find the y - intercept $b$

Use the slope - intercept form $y=mx + b$ and substitute one of the points, say $(x = 8,y=-7)$ and $m=-\frac{1}{4}$. Then $-7=-\frac{1}{4}\times8 + b$. Simplify the right - hand side: $-\frac{1}{4}\times8=-2$, so $-7=-2 + b$. Solving for $b$ gives $b=-7 + 2=-5$.

Step4: Write the equation of the line

The slope - intercept form is $y=mx + b$. Substituting $m = -\frac{1}{4}$ and $b=-5$ gives $y=-\frac{1}{4}x-5$.

Answer:

$y = -\frac{1}{4}x-5$