Question

What is an equation of the line that passes through the points (−5,−7) and (5,1)?

Answer 1

y =
`(4)/(5)` x - 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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (5, 1)

m =
`(1+7)/(5+5)` =
`(8)/(10)` =
`(4)/(5)`, thus

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

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

Using (5, 1), then

1 = 4 + c ⇒ c = 1 - 4 = - 3

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