Question

What is an equation for the line that passes through (6. -5) and (-8, 16)?
y=+*+28

Answer 1

y = -
`(3)/(2)` x + 4

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 )

with (x₁, y₁ ) = (6, - 5) and (x₂, y₂ ) = (- 8, 16)

m =
`(16+5)/(-8-6)` =
`(21)/(-14)` = -
`(3)/(2)`, thus

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

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

Using (- 8, 16), then

16 = 12 + c ⇒ c = 16 - 12 = 4

y = -
`(3)/(2)` x + 4 ← equation of line