Answer:
The slope of g(x) is: [tex]m=0[/tex]
The slope of f(x) is: [tex]m-1[/tex]
Step-by-step explanation:
For this exercise you need to know that:
1. By definition the slope of any horizontal line is zero ([tex]m=0[/tex])
2. The slope of a line can be calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, you can observe in the graph of the function g(x) given in the exercise that it is an horizontal line. Then, based on the explanation given before, you can conclude that its slope is:
[tex]m=0[/tex]
To find the slope of the function f(x) shown in the table attached, you need to follow these steps:
- Choose two points from the table:
[tex](0,3)[/tex] and [tex](4,-1)[/tex]
- You can say that:
[tex]y_2=-1\\y_1=3\\\\x_2=4\\x_1=0[/tex]
- Substitute values into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]:
[tex]m=\frac{-1-3}{4-0}[/tex]
- Finally, evaluating, you get:
[tex]m=\frac{-4}{4}\\\\m=-1[/tex]
