Question

what equation in slope-intercept form represents the line that passes through the points (3,5) and (-9,2)

Answer 1

y =
`(1)/(4)` x +
`(17)/(4)`

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (- 9, 2)

m =
`(2-5)/(-9-3)` =
`(-3)/(-12)` =
`(1)/(4)`

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

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

using (3, 5), then

5 =
`(3)/(4)` + c ⇒ c = 5 -
`(3)/(4)` =
`(17)/(4)`

y =
`(1)/(4)` x +
`(17)/(4)` ← in slope- intercept form