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
