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Chapter 1: Q. 127 (page 43)

The equation 2x-y=Cdefines 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=0and C=2. Can you draw a conclusion from the graph about each member of the family?

Short Answer

Expert verified

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

Step by step solution

01

Given information

We are given a family of lines represented by equation2x-y=C

02

Find the different equations

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

When C=-4we get,

2x-y=-4y=2x+4

When c=0we get,

2x-y=0y=2x

When C=2we get,

2x-y=Cy=2x-2

03

Plot the graph

The graph of family of lines can be given as

04

Conclusion

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

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Most popular questions from this chapter

Tell whether the given points are on the graph of the equation.

Equation:y2=x2+9Points:(0,3);(3,0);(-3,0)

Find the midpoint of the line segment joining the points P1 and P2 .

P1=(3,-4);P2=(5,4)

True or false The point 1,2is on the line2x+y=4.

Find the distance d(P1,P2)between the points P1andP2.

P1=(4,-3);P2=(6,4)

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(-2,3);(2,1)
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