Question

Which graph models the equation 2x + 3y = 6?

Answer 1

given 2x + 3y = 6

We can find the intercepts, that is where the graph crosses the x and y axes

• let x = 0, in the equation for y-intercept

• let y = 0, in the equation for x-intercept

x = 0 : 3y = 6 ⇒ y = 2 ⇒ (0, 2) ← y-intercept

y = 0 : 2x = 6 ⇒ x = 3 ⇒ (3, 0) ← x -intercept

Expressing the equation in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

3y = - 2x + 6 ( divide all terms by 3 )

y = - $\frac{2}{3}$ x + 2

m is negative indicating the graph slopes down from left to right

The graph sloping down from left to right , crossing the x-axis at (3, 0) and the y-axis at (0, 2) is the graph which models the given equation.