Question

what is the slope- intercept form of the equation of the line that passes through the points (-3,2) and(1,5)

Answer 1

y =
`(3)/(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 gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

m =
`(5-2)/(1+3)` =
`(3)/(4)`, hence

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

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

using (1, 5 ), then

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

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