Question

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

Answer 1

Answer:

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

2. F(x) = 3x - 9

Answer 2

Answer:

see explanation

Step-by-step 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 = $\frac{4+1}{4-0}$ = $\frac{5}{4}$

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

y = $\frac{5}{4}$ x - 1 ← in slope- intercept form

(2)

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

m = $\frac{-6-3}{1-4}$ = $\frac{-9}{-3}$ = 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