Question

Write an equation that represents the line. (-3,-6) and (2,-2) use exact numbers

Answer 1

Given:

The line passes through (-3,-6) and (2,-2).

To find:

The equation of line.

Solution:

If a line passes through two points
`(x_1,y_1)\text{ and }(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through (-3,-6) and (2,-2). So, the equation of line is

`y-(-6)=(-2-(-6))/(2-(-3))(x-(-3))`

`y+6=(-2+6)/(2+3)(x+3)`

`y+6=(4)/(5)(x+3)`

`y+6=(4)/(5)(x)+(4)/(5)(3)`

Subtract 6 from both sides.

`y=(4)/(5)(x)+(12)/(5)-6`

`y=(4)/(5)(x)+(12-30)/(5)`

`y=(4)/(5)(x)+(-18)/(5)`

`y=(4)/(5)(x)-(18)/(5)`

Therefore, the equation of line is
`y=(4)/(5)(x)-(18)/(5)`.