Given the equation below
[tex]3x+y=-9[/tex]
To find the intercepts of the graph of the equation above. The following steps will be used.
Step 1: To obtain the x-intercept, set y=0 and solve for x
[tex]\begin{gathered} 3x+y=-9 \\ y=0 \\ 3x+0=-9 \\ 3x=-9 \\ \frac{3x}{3}=-\frac{9}{3} \\ x=-3 \\ x-\text{intercept}\Rightarrow(-3,0) \end{gathered}[/tex]
Hence, the x-intercept is (-3,0)
Step 2: To find the y-intercept, set x= 0 and solve the equation to find y.
[tex]\begin{gathered} 3x+y=-9 \\ x=0 \\ 3(0)+y=-9 \\ y=-9 \\ y-\text{intercept}\Rightarrow(0,-9) \end{gathered}[/tex]
Hence, the y-intercept is (0,-9)
The graph of the equation showing the intercepts is shown below
