Question

Which of the following equations describes the
graph below?

Answer 1

5x + 3y = - 15

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 ) = (- 3, 0) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m =
`(-5-0)/(0-(-3))` =
`(-5)/(0+3)` = -
`(5)/(3)`

the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = -
`(5)/(3)` x - 5 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 5x - 15 ( add 5x to both sides )

5x + 3y = - 15 ← in standard form