Question

What is an equation of the line that passes through the points (-6, -2) and (-3, -3)?

Answer 1

`y = - (1)/(3) x - 4`

Explanation:

The equation of a kind can be written in the slope intercept form, y= mx +c, where m is the gradient and c is the y-intercept.

`\boxed{gradient = (y1 - y2)/(x1- x2) }`

`m = ( - 2 - ( - 3))/( - 6 - ( - 3))`

`m = ( - 2 + 3)/( - 6 + 3)`

`m = ( 1)/( - 3)`

Substitute the value of m into the equation:

`y = - (1)/(3) x + c`

To find the value of c, substitute a pair of coordinates.

When x= -3, y= -3,

`- 3 = - (1)/(3) ( - 3) + c`

`- 3 = 1 + c`

c= -3 -1

c= -4

∴ The equation of the line is
`y = - (1)/(3) x -4`.