Question

1. Write the equation of the line that passes through (8 , - 20) and (5 , - 2). Show all steps of the work.

Answer 1

`\huge\boxed{y=-6x+28}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

`m` - slope

`(x_1;\ y_1)` - point on a line

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

`(x_1;\ y_1);\ (x_2;\ y_2)` - points on a line

We have two points:

`(8;\ -20);\ (5;\ -2)`

Calculate the slope:

`m=(-2-(-20))/(5-8)=(-2+20)/(-3)=(18)/(-3)=-6`

Substitute to the equation of a line:

`y-(-20)=-6(x-8)`

`y+20=-6x+48` subtract 20 from both sides

`y=-6x+28`