Answer:
[tex]y=\frac{1}{2}x-6[/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 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 (2,-5) and (8,-2)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-(-5)}{8-2}\\=\frac{-2+5}{8-2}\\=\frac{3}{6}\\=\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]-5=\frac{1}{2}(2)+b\\-5=1+b[/tex]
Subtract 1 from both sides to isolate b
[tex]-5-1=1+b-1\\-6=b[/tex]
Therefore, the y-intercept of the line is -6. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x+(-6)\\y=\frac{1}{2}x-6[/tex]
I hope this helps!