Question

What is the equation of the line that goes through (-3,-1) and (3,3)?

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 ) = (- 3, - 1) and (x₂, y₂ ) = (3, 3)

m =
`(3+1)/(3+3)` =
`(4)/(6)` =
`(2)/(3)`, thus

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

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

Using (3, 3), then

3 = 2 + c ⇒ c = 3 - 2 = 1

y =
`(2)/(3)` x + 1 ← equation of line

Multiply through by 3

3y = 2x + 3 ( subtract 3y from both sides )

0 = 2x - 3y + 3 ( subtract 3 from both sides )

- 3 = 2x - 3y, that is

2x - 3y = - 3 ← in standard form