Question

Find the equation that passes through (5,2) and (2, -4)

Answer 1

y = 2x - 8

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 ) = (5, 2) and (x₂, y₂ ) = (2, - 4)

m =
`(-4-2)/(2-5)` =
`(-6)/(-3)` = 2 , then

y = 2x + c ← is the partial equation

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

Using (5, 2 ), then

2 = 10 + c ⇒ c = 2 - 10 = - 8

y = 2x - 8 ← equation of line

Answer 2

equation 1st lies in 1st quadrant 5 = x and y= 2

as well as second one is lie on 4th quadrant