Question

2x+3y=-6 find the x- and y- Intercepts of the graph of the equation

Answer 1

`\begin{gathered} x-intercept\colon x=-3 \\ y-intercept\colon y=-2 \end{gathered}`

1) Since we need to find the x-intercepts of this equation, let's do it algebraically and then on the graph. Plug y=0 into that equation and then solve it for x:

`\begin{gathered} 2x+3(0)=-6 \\ 2x=-6 \\ (2x)/(2)=-(6)/(2) \\ x=-3 \end{gathered}`

2) Now, let's find the y-intercept. We just need to plug into that x=0

`\begin{gathered} 2(0)+3y=-6 \\ 3y=-6 \\ (3y)/(3)=(-6)/(3) \\ y=-2 \end{gathered}`

Notice that we solved this in 2 steps. We can check by plotting that using the points we have just found (-3,0) and (0,-2) :