Question

What is the slope-intercept form of (-2,1) and (4,6)

Answer 1

y =
`(5)/(6)` x +
`(8)/(3)`

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 ) = (- 2, 1) and (x₂, y₂ ) = (4, 6)

m =
`(6-1)/(4+2)` =
`(5)/(6)` , thus

y =
`(5)/(6)` x + c ← is the partial equation

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

Using (4, 6 ), then

6 =
`(20)/(6)` + c ⇒ c = 6 -
`(20)/(6)` =
`(16)/(6)` =
`(8)/(3)`

y =
`(5)/(6)` x +
`(8)/(3)` ← equation of line