Question

Can someone help me with my practice question? I'm unsure of the answer.

Answer 1

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:

`\begin{gathered} (3)/(2)x-(1)/(2)y=-3 \\ (3)/(2)\cdot0-(1)/(2)y=-3 \\ (-1)/(2)y=-3 \\ y=-3\cdot(-2)=6 \end{gathered}`

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:

`\begin{gathered} (3)/(2)x-(1)/(2)y=-3 \\ (3)/(2)x-(1)/(2)\cdot0=-3 \\ (3)/(2)x=-3 \\ x=-3\cdot(2)/(3)=-2 \end{gathered}`

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.