Question

What is the equation that represents the line?

Answer 1

see explanation

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 6) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line

m =
`(-3+6)/(2+2)` =
`(3)/(4)`, thus

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

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

Using (2, - 3), then

- 3 =
`(3)/(2)` + c ⇒ c = - 3 -
`(3)/(2)` = -
`(9)/(2)`

y =
`(3)/(4)` x -
`(9)/(2)` ← equation of line