Question

Graph two more functions in the same family

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

We know that the slope-intercept of the line equation is

$y = mx + b$

where m is the slope and b is the y-intercept

Please note that a linear equation contains no powers of x besides.

For example, the equation of the form

y = 2x+3

has the slope m = 2 and y-intercept b = 3

The graph is shown below.

Let us graph two more functions of the same family by changing the parameter of y-intercept b.

Graphing y = 2x+5

y = 2x + 5

has same slope m = 2. But, the y-intercept b = 5

The graph of y = 2x+5 is attached below.

Graphing y = 2x+7

y = 2x + 7

has same slope m = 2. But, the y-intercept b = 7

The graph of y = 2x+7 is attached below.

Thus, we would have the following graphs of the family of linear functions.

• y = 2x+3

• y = 2x + 5

• y = 2x + 7

Please notice that all the functions have the same slope m = 2. Thus, all the lines would be parallel.

Thus, from the graph, it is clear that:

• The red line represents the function y = 2x+3 with the y-intercept (0, 3)

• The blue line represents the function y = 2x+5 with the y-intercept (0, 5)

• The green line represents the function y = 2x+7 with the y-intercept (0, 7)

The graph is attached below.