Question

what is the equation, in slope- intercept form, of the line that contains the points (-3,4) and (5,7)

Answer 1

y =
`(3)/(8)` x +
`(41)/(8)`

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 the slope use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (5, 7)

m =
`(7-4)/(5+3)` =
`(3)/(8)`, hence

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

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

using (5, 7 ), then

7 =
`(15)/(8)` + c ⇒ c = 7 -
`(15)/(8)` =
`(41)/(8)`

y =
`(3)/(8)` x +
`(41)/(8)` ← equation in slope-intercept form