Question

Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)

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 ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)

m =
`(-5-4)/(2+10)` =
`(-9)/(12)` = -
`(3)/(4)`, thus

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

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

Using (2, - 5), then

- 5 = -
`(3)/(2)` + c ⇒ c = - 5 +
`(3)/(2)` = -
`(7)/(2)`

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