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Sagot :
Answer:
f(x) = 12x = 10
Step-by-step explanation:
We need a linear equation in the slope-intercept form.
y = mx + b
where y = total pay, m = hourly salary, x = number of hours worked, and b = y-intercept, or initial value
Let's look in the table.
1 hour: $22
2 hours: $34
The difference in pay between 1 hour and 2 hours is $34 - $22 = $12.
The difference in time between 1 hour and 2 hours is 1 hour.
In 1 hour he earns $12. That means the slope is 12.
We know he earns $22 for working a total of 1 hour.
Start at 1 hour and $22 on the table.
Subtract 1 hour from 1 hour to get 0 hours.
Subtract $12 form $22 to get $10.
That means for 0 hours he gets $10. b = 10
The equation is
y = 12x + 10
In function form, we have:
f(x) = 12x = 10
Here we want to find a linear relation with only using the data in a table, we will find that the line is:
[tex]y = 12\cdot x + 12[/tex]
We know that Damian's earns a set amount plus an hourly wage, then this can be modeled with a linear equation:
[tex]y = a\cdot x + b[/tex]
Where a is the slope, which in this case is the hourly wage, and b is the y-intercept, which in this case is the set amount.
Such that x is the number of hours and y is the pay.
We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be given as:
[tex]a = \frac{x_2 - x_1}{y_2 - y_1}[/tex]
By looking at the table we can find two points of our line, for example, if we use the first and third points:
(1, 22) and (2, 34) then the slope will be:
[tex]a = \frac{34 - 22}{2 - 1} = 12[/tex]
Then the line is something like:
[tex]y = 12\cdot x + b[/tex]
To find the value of b, we can use one of the points, for example, the point (1, 22) means that when x = 1, we must have y = 22.
Replacing that in the above equation we have:
[tex]22 = 12\cdot1 + b\\\\22 = 12 + b\\\\22 - 12 = b = 12[/tex]
Then the equation of the line is:
[tex]y = 12\cdot x + 12[/tex]
If you want to learn more, you can read:
https://brainly.com/question/22901085
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