Answer:
Please check the explanation.
Step-by-step explanation:
We know that the slope-intercept of the line equation is
[tex]y = mx + b[/tex]
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.
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.
