Answer:
The equation of the line is:
[tex]y=-3x+4[/tex]
Please check the attached graph.
Step-by-step explanation:
x y
-1 7
2 -2
7 -17
10 -26
Taking two points (-1, 7) and (2, -2) to find the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-1,\:7\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)[/tex]
[tex]m=\frac{-2-7}{2-\left(-1\right)}[/tex]
Refine
[tex]m=-3[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -3 and the point (-1, 7)
[tex]y-7=-3\left(x-\left(-1\right)\right)[/tex]
[tex]y-7=-3\left(x+1\right)[/tex]
Add 7 to both sides
[tex]y-7+7=-3\left(x+1\right)+7[/tex]
Simplify
[tex]y=-3x+4[/tex]
Therefore, the equation of the line is:
[tex]y=-3x+4[/tex]
Please check the attached graph.
