Answer:
[tex]y=-\frac{1}{2}x-3[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (6,-6) and (-2,-2)
[tex]=\frac{-2-(-6)}{-2-6}\\=\frac{-2+6}{-2-6}\\=\frac{4}{-8}\\=-\frac{1}{2}[/tex]
Therefore, the slope of the line is [tex]-\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{1}{2}x+b[/tex]
Plug in one of the given points and solve for b
[tex]-6=-\frac{1}{2}(6)+b\\-6=-3+b[/tex]
Add 3 to both sides
[tex]-6+3=-3+b+3\\-3=b[/tex]
Therefore, the y-intercept of the line is -3. Plug this back into [tex]y=-\frac{1}{2}x+b[/tex]:
[tex]y=-\frac{1}{2}x-3[/tex]
I hope this helps!
