Question

Find the equation of the line that passes through (9,-4) and (-1,-8).

Answer 1

`y = (2)/(5) x - 7 (3)/(5)`

Explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the y-intercept.

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

Gradient

`= ( - 4 - ( - 8))/(9 - ( - 1))`

`= ( - 4 + 8)/(9 + 1)`

`= (4)/(10)`

`= (2)/(5)`

Substitute the value of the gradient into the equation:

`y = (2)/(5) x + c`

To find the value of the y-intercept, substitute a pair of coordinates.

When x= -1, y= -8,

`- 8 = (2)/(5) ( - 1) + c`

`- 8 = - (2)/(5) + c`

`c = - 8 + (2)/(5)`

`c = - 7 (3)/(5)`

Thus the equation of the line is
`y = (2)/(5) x - 7 (3)/(5)`.