Formulas For Linear Functions. Can Anyone Me Understand This Problem?

In summary: PIn summary, the conversation discusses an insurance salesperson's annual earnings, which includes a base salary and a commission based on the premiums sold. The question asks for the slope and y-intercept of this function, and the suggested equation is 12000+.03X. However, this equation does not include an 'equals' sign and does not specify the value of x, making it not very rigorous.
  • #1
dmbeluke
6
0
I am stuck. I've gone through all my notes to try and figure out how to do this problem, with no success. Any help would be appriciated. Thank you!


An insurance salesperson earns an annual salary of $12,000 plus a commission equal to 3% of the premiums on all policies sold. If f(x) is a function which gives her annual earnings, what is the slope of f(x)? What is the y-intercept? Find the equation for f(x).


The equation I came up with was:
12000+.03X

This is as far as I have gotten.
 
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  • #2
Hint

Your equation is correct.

Note the two numbers in your equation. One of them is the answer to one of the questions, and the other is the answer to the other question.
 
  • #3
Just a minor detail:
12000+.03X is not an "equation" (there's no 'equals' sign on it).
You can call it a function , or an expression.
 
  • #4
You also ought to specify what x is (we presume it is the value of the premiums she sells).

Then of course I'd like to argue that seeing as these quantities are all discrete (she preusmably doesn't sell 120,000.02939430854324359 worth of premiums in whatever currency we're dealing with, and she'll have a funny bank account that goes to more than two decimal places) that the question ought to be excised from the book/homework sheet as being not particularly rigorous.
 

1. What is a linear function?

A linear function is a mathematical function that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. It represents a straight line on a graph and can be used to model relationships between two variables.

2. How do I determine the slope of a linear function?

The slope of a linear function is represented by the m in the equation y = mx + b. To determine the slope, you can use the formula m = (y2 - y1) / (x2 - x1), where x1 and y1 are the coordinates of one point on the line, and x2 and y2 are the coordinates of another point on the line.

3. What is the y-intercept and how do I find it?

The y-intercept is the point where the line intersects the y-axis on a graph. It is represented by the b in the equation y = mx + b. To find the y-intercept, you can either look at the equation and identify the value of b, or you can plot the line on a graph and see where it crosses the y-axis.

4. How do I graph a linear function?

To graph a linear function, you need to plot at least two points on the line. You can do this by choosing any values for x and plugging them into the equation y = mx + b to solve for y. Once you have two points, you can connect them with a straight line to create the graph of the linear function.

5. How can I use linear functions in real life?

Linear functions are used to model many real-life situations, such as calculating the cost of a phone plan based on the number of minutes used, predicting the growth of a population over time, or determining the distance a car can travel based on its speed. They are also used in industries such as economics, engineering, and physics to analyze and make predictions about various systems and processes.

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