Answer:
[tex]y=\displaystyle- \frac{1}{2} x+1[/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=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4,3) and (-8,5):
[tex]m=\displaystyle\frac{3-5}{-4-(-8)}\\\\m=\displaystyle\frac{-2}{-4+8}\\\\m=\displaystyle\frac{-2}{4}\\\\m=\displaystyle- \frac{1}{2}[/tex]
Therefore, the slope of the line is [tex]\displaystyle- \frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle- \frac{1}{2} x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle- \frac{1}{2} x+b[/tex]
Plug in one of the points and solve for b:
[tex]3=\displaystyle- \frac{1}{2} (-4)+b\\\\3=2+b\\b=1[/tex]
Therefore, the y-intercept is 1. Plug this back into the equation:
[tex]y=\displaystyle- \frac{1}{2} x+1[/tex]
I hope this helps!
