Question

Damian works after school. Each
day he earns a set amount, plus
an hourly wage, as shown in the
table Write a linear function i
that Damian can use to determine
his pay.

Answer 1

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

Answer 2

Here we want to find a linear relation with only using the data in a table, we will find that the line is:

$y = 12\cdot x + 12$

We know that Damian's earns a set amount plus an hourly wage, then this can be modeled with a linear equation:

$y = a\cdot x + b$

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:

$a = \frac{x_2 - x_1}{y_2 - y_1}$

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:

$a = \frac{34 - 22}{2 - 1} = 12$

Then the line is something like:

$y = 12\cdot x + b$

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:

$22 = 12\cdot1 + b\\\\22 = 12 + b\\\\22 - 12 = b = 12$

Then the equation of the line is:

$y = 12\cdot x + 12$

If you want to learn more, you can read:

https://brainly.com/question/22901085