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 = - [tex]\frac{2}{3}[/tex] 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.
