Question

The equation of the linear graph that passes through (2, -2) and (-2, -7)

Answer 1

y =
`(5)/(4)` x -
`(9)/(2)`

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, - 2) and (x₂, y₂ ) = (- 2, - 7)

m =
`(-7+2)/(-2-2)` =
`(-5)/(-4)` =
`(5)/(4)` , thus

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

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

Using (2, - 2) , then

- 2 =
`(5)/(2)` + c ⇒ c = - 2 -
`(5)/(2)` = -
`(9)/(2)`

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