Question

Which equation has the graph shown below? (-4,0) (0,2)

Answer 1

- 4x + 8y = 16

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 ) = (- 4, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m =
`(2-0)/(0-(-4))` =
`(2)/(0+4)` =
`(2)/(4)`

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y =
`(2)/(4)` x + 2 ( multiply through by 4 to clear the fraction )

4y = 2x + 8 ( subtract 2x from both sides )

- 2x + 4y = 8 ( multiply through by 2 )

- 4x + 8y = 16