Q. 127 - Precalculus Enhanced with Graphing Utilities

Question

The equation $2x-y=C$ defines a family of lines, one line for each value of $C$. On one set of coordinate axes, graph the members of the family when $C=-4,C=0$ and $C=2$. Can you draw a conclusion from the graph about each member of the family?

Step-by-Step Solution

Answer

We conclude that the liens are parallel as they have same slope but have different y-intercept

Step 1: Given information

We are given a family of lines represented by equation $2x-y=C$

Step 2: Find the different equations

To find the different equation we put the given different values of $C$

When $C=-4$ we get,

$$\begin{gathered} 2x-y=-4 \\ y=2x+4 \end{gathered}$$

When $c=0$ we get,

$$\begin{gathered} 2x-y=0 \\ y=2x \end{gathered}$$

When $C=2$ we get,

$$\begin{gathered} 2x-y=C \\ y=2x-2 \end{gathered}$$

Step 3: Plot the graph

The graph of family of lines can be given as

Step 4: Conclusion

From the graph and equation we conclude that the lines are parallel and have different y-intercept