The intercepts are the points where the line intercept one of the axis. That's why we have y-intercepts and x-intercepts.
To calculate them in a equation line, we make one of the variables equal to 0 and calculate the value of the other variable. Then we have the point in which the axis is intercepted.
For example, the y-intercept happens when x=0. This is when the line cross the vertical axis.
We can calculate the y-intercept replacint x by 0 in the equation:
[tex]\begin{gathered} \frac{3}{2}x-\frac{1}{2}y=-3 \\ \frac{3}{2}\cdot0-\frac{1}{2}y=-3 \\ \frac{-1}{2}y=-3 \\ y=-3\cdot(-2)=6 \end{gathered}[/tex]
The point where the line intercepts the vertical axis is (x,y)=(0, 6).
Then, we can calculate the x-intercept replacing y by 0 in the equation:
[tex]\begin{gathered} \frac{3}{2}x-\frac{1}{2}y=-3 \\ \frac{3}{2}x-\frac{1}{2}\cdot0=-3 \\ \frac{3}{2}x=-3 \\ x=-3\cdot\frac{2}{3}=-2 \end{gathered}[/tex]
Then, we know that the line intercepts the x-axis in the point (x,y)=(-2, 0)
We can graph this two points and the line that does through them is the line described by the equation we are working on.
If we graph it, we get:
We can see, just by looking at the two points, that the slope is positive, as y increases when x increases.
