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 = [tex]\frac{4+1}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]
Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1
y = [tex]\frac{5}{4}[/tex] x - 1 ← in slope- intercept form
(2)
let (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (1, - 6), then
m = [tex]\frac{-6-3}{1-4}[/tex] = [tex]\frac{-9}{-3}[/tex] = 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
