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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.2, Problem 5E

(a)

To determine

**To find:** An equation of the family of linear function with slope 2 and sketch the members of the family on the graph.

Expert Solution

An equation for the family of linear function with slope 2 is

The general equation of a linear function is of the form *m* and *y*-intercept *c*.

Given that, the slope (*m*) is 2.

Thus, the linear function of slope 2 is

Obtain the equations for the various *c* values.

If

If

If

If

Draw the graph of the above equations as shown below in Figure 1.

From Figure 1, it is noticed that all the members of the family of linear function *m* = 2.

(b)

To determine

**To find:** The equation of the family of linear function satisfying the condition that

Expert Solution

The equation for the family of linear function with the condition

The general equation of a linear function is of the form *m* and *y*-intercept *c*.

Since the equation satisfies the condition

Substitute the point

Thus, the required linear function is

Obtain the equations for the various *m* values.

If

If

If

If

Draw the graph of the above equations as shown below in Figure 2.

From Figure 2, it is noticed that all the members of the family of linear function

(c)

To determine

**To find:** The common function belongs to both the families of part (a) and part (b).

Expert Solution

The common function belongs to both the families is

The function that belongs to both families, must satisfies the conditions that the slope, *m* = 2 and

Substitute *m* = 2 and the point

Thus, the required function is

The graph of the function

From Figure 3, it is observed that the conditions of both parts (a) and (b) are satisfied. That is, the graph of slope 2 and passing through the point (2, 1).