Answer:
[tex]y=-\frac{1}{2}x-8[/tex]
Step-by-step explanation:
[tex](-4,-6)(-2,-7)[/tex]
Step 1. Find the slope (by using the slope-formula)
m = slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7--6}{-2--4}[/tex]
[tex]m=\frac{-1}{2}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Step 2. Create the equation of a line that has a slope of [tex]-\frac{1}{2}[/tex]
[tex]y=-\frac{1}{2} x+b[/tex]
Step 3. Find the y-intercept
To do this, use any of the two points and substitute their x and y values
[tex]y=-\frac{1}{2}x+b[/tex]
point: [tex](-2,-7)[/tex]
[tex](-7)=-\frac{1}{2}(-2)+b[/tex]
[tex](-7)=1+b[/tex]
[tex]b=-7-1[/tex]
[tex]b=-8[/tex]
Step 4. Write the equation in Slope-intercept form
[tex]y=mx+b[/tex]
[tex]y=-\frac{1}{2} x-8[/tex]
