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Answer:
[tex]y=-3x+7[/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 x=0)
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 points (2,1) and (5,-8):
[tex]m=\displaystyle \frac{-8-1}{5-2}\\\\m=\displaystyle \frac{-9}{3}\\\\m=-3[/tex]
Therefore, the slope of the line is -3. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=-3x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=3x+b[/tex]
Plug in one of the given points and solve for b:
[tex]1=-3(2)+b\\1=-6+b\\b=7[/tex]
Therefore, the y-intercept is 7. Plug this back into [tex]y=-3x+b[/tex]:
[tex]y=-3x+7[/tex]
I hope this helps!