Question

Write an equation for the line that passes through the points (-8,5) and (-2,9) in slope-intercept form.

Answer 1

y =
`(2)/(3)` x +
`(31)/(3)`

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (- 2, 9)

m =
`(9-5)/(-2+8)` =
`(4)/(6)` =
`(2)/(3)` , thus

y =
`(2)/(3)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 2, 9 ), then

9 = -
`(4)/(3)` + c ⇒ c = 9 +
`(4)/(3)` =
`(31)/(3)`

y =
`(2)/(3)` x +
`(31)/(3)` ← equation of line