Question

Write an equation of the line through each pair of points in slope-intercept form.

1. (0,-1) (4,4)
2. (4,3) (1,-6)​

Answer 1

see explanation

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 = (y₂ - y₁ ) / (x₂ - x₁ )

(1)

let (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 4), then

m =
`(4+1)/(4-0)` =
`(5)/(4)`

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y =
`(5)/(4)` x - 1 ← in slope- intercept form

(2)

let (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (1, - 6), then

m =
`(-6-3)/(1-4)` =
`(-9)/(-3)` = 3, hence

y = 3x + c ← is the partial equation

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

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9

y = 3x - 9 ← in slope- intercept form

Answer 2

1. F(x) = 5/4 x - 1

2. F(x) = 3x - 9