Question

two points are plotted on the grid. slope: ____ y - intercept: ____ what is the equation of the line that passes through the two points?

Explanation:

Step1: Identify the two points

Let the two points be $(-8,2)$ and $(8, - 4)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1=-8,y_1 = 2,x_2 = 8,y_2=-4$ into the formula: $m=\frac{-4 - 2}{8-(-8)}=\frac{-6}{16}=-\frac{3}{8}$.

Step3: Use the point - slope form to find the y - intercept

The point - slope form is $y - y_1=m(x - x_1)$. Use the point $(-8,2)$ and $m =-\frac{3}{8}$. So $y - 2=-\frac{3}{8}(x + 8)$. Expand the right - hand side: $y-2=-\frac{3}{8}x-3$. Add 2 to both sides to get $y=-\frac{3}{8}x - 1$. The y - intercept $b=-1$.

Step4: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Since $m =-\frac{3}{8}$ and $b=-1$, the equation of the line is $y=-\frac{3}{8}x-1$.

Answer:

Slope: $-\frac{3}{8}$
Y - intercept: $-1$
Equation of the line: $y =-\frac{3}{8}x-1$