Question

What is an equation of the line that passes through the points (6, 8) and
(-3, 2)?

Answer 1

y =
`(2)/(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, 8) and (x₂, y₂ ) = (- 3, 2)

m =
`(2-8)/(-3-6)` =
`(-6)/(-9)` =
`(2)/(3)` , thus

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

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

Using (6, 8), then

8 = 4 + c ⇒ c = 8 - 4 = 4

y=
`(2)/(3)` x + 4 ← equation of line