We have the expression
[tex]3x+9y=9[/tex]We can find the intercepts using the equation, and then check them graphically.
The y-intercept happens when x=0, because that is the definition of the y-axis.
Then, replacing x with 0 in the equation, gives us the value of the y-intercept:
[tex]\begin{gathered} 3\cdot0+9y=9 \\ y=\frac{9}{9}=1 \end{gathered}[/tex]The y-intercept is y=1.
For the x-intercept, we have y=0. We repeat the procedure and get:
[tex]\begin{gathered} 3x+9\cdot0=9 \\ x=\frac{9}{3}=3 \end{gathered}[/tex]The x-intercept is x=3.
We can check it with the graph:
We have there the x and y intercepts (x=3 and y=1).
