Question

What is an equation of the line that passes through the points (-6, -4) and (3, 8)

Answer 1

y =
`(4)/(3)` 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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 6, - 4) and (x₂, y₂ ) = (3, 8)

m =
`(8-(-4))/(3-(-6))` =
`(8+4)/(3+6)` =
`(12)/(9)` =
`(4)/(3)` , then

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

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

Using (3, 8 ) , then

8 = 4 + c ⇒ c = 8 - 4 = 4

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