Using a linear function, we have that:
a) The values are: a = 11 and b = 5.
b) The rule is:
[tex]y = 3x + 2[/tex]
c) The value of the output is 62.
d) The value of the input is 25.
The equation of a linear function is given by:
[tex]y = mx + b[/tex]
In which
- m is the slope, which is the rate of change.
- b is the y-intercept, which is the initial value.
First, we are going to solve item b to find the rule, then we solve other items.
Item b:
In the table, we have two points: (1,5) and (2,8).
The slope is given by change in y divided by change in x, thus:
[tex]m = \frac{8 - 5}{2 - 1} = 3[/tex]
Then
[tex]y = 3x + b[/tex]
Point (1,5) means that when [tex]x = 1, y = 5[/tex], and this is used to find b.
[tex]5 = 3(1) + b[/tex]
[tex]b = 2[/tex]
Thus, the rule is:
[tex]y = 3x + 2[/tex]
Item a:
a is the value of y when x = 3, thus:
[tex]y = a = 3(3) + 2 = 11[/tex]
Thus, a = 11.
b is the value of x when y = 17, thus:
[tex]3b + 2 = 17[/tex]
[tex]3b = 15[/tex]
[tex]b = 5[/tex]
The values are: a = 11 and b = 5.
Item c:
The value of the output is y when x = 20, thus:
[tex]y = 3(20) + 2 = 60 + 2 = 62[/tex]
Thus, the value of the output is 62.
Item d:
The value of the input is x when y = 77, thus:
[tex]3x + 2 = 77[/tex]
[tex]3x = 75[/tex]
[tex]x = \frac{75}{3}[/tex]
[tex]x = 25[/tex]
The value of the input is 25.
A similar problem is given at https://brainly.com/question/25004958
