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The equation 2x - y = C defines a family of lines, one

Chapter , Problem 2.3.127

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QUESTION:

The equation \(2 x-y=C\) 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?

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QUESTION:

The equation \(2 x-y=C\) 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?

ANSWER:

Step 1 of 3

Given equation representing the family of straight lines is

\(2 x-y=C \quad (i)\)

To draw lines for \(C=-4, C=0\) and C = 2.

By plugging \(C=-4\) in equation (i) it results

\(2 x-y=-4 \quad \quad (ii)\)

The graph of the line represented in equation (ii) is shown below

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