Question

Create a linear equation for the following data:

y = 2x – 9

y = -3x + 7

y = -3x + 4

Answer 1

The equation of the line is:

`y=-3x+4`

Please check the attached graph.

Explanation:

x y

-1 7

2 -2

7 -17

10 -26

Taking two points (-1, 7) and (2, -2) to find the slope

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-1,\:7\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)`

`m=(-2-7)/(2-\left(-1\right))`

Refine

`m=-3`

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -3 and the point (-1, 7)

`y-7=-3\left(x-\left(-1\right)\right)`

`y-7=-3\left(x+1\right)`

Add 7 to both sides

`y-7+7=-3\left(x+1\right)+7`

Simplify

`y=-3x+4`

Therefore, the equation of the line is:

`y=-3x+4`

Please check the attached graph.