carlosramirez04
Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.

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 Hi class=

Sagot :

mathstudent55

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

facundo3141592

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

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.