How can you model data with a linear function? You must provide a real-world example and show how to model the problem using a linear function. Be sure to explain how you know it is a function.
This is a discussion question I need help on, can somebody please help me understand how and where to begin? Thanks
I just paid $11.04 for 12 litres of gas, while last week I paid $$59.80 for 65 litres of gas at the same price.
If L is the number of litres, and C is the cost in dollars per L, find the equation for the cost in terms of L
So you have 2 points of the form (L,C) and they are (12, 11.04) and (65, 59.80)
step 1:
find the slope :
slope = (59.8-11.04)/(65-12) = .92
since we know that for 0 L of gas , I would pay $0.00, the relations is a direct variation and it is
C = .92L
Remember a linear function is graphed by a straight line.
Pick different values of L, then find C
Plot those points, showing a straight line
Okay, thank you Reiny!:)
Wait... isn't a function supposed to go like: y = f(x) or something? Where does that come in to play here?
Do you like
C(L) = .92L better?
so the horizontal axis will be labeled L
and the vertical axis as C(L)
To model data with a linear function, you need to understand what a linear function represents and how it can be applied to real-world scenarios.
A linear function is a mathematical relationship between two variables, where the output (dependent variable) varies linearly with respect to the input (independent variable). In other words, when you plot the data points on a graph, they will form a straight line.
Let's consider a real-world example to illustrate this. Suppose you want to model the relationship between the number of hours a person studies and their test score. You gather data from several students and record the number of hours they studied and their corresponding test scores.
Here's a step-by-step process to model this problem using a linear function:
1. Collect your data: Record the number of hours studied by each student along with their respective test scores.
2. Plot the data: Create a scatter plot with the number of hours studied on the x-axis and the test scores on the y-axis. Each data point will represent a student's study time and test score.
3. Visual inspection: Look at the scatter plot and check if the data pattern appears to be linear. If the data points seem to generally align in a straight line, it suggests a linear relationship between the variables.
4. Calculate the line of best fit: Determine the line that best represents the relationship between the variables. This line is called the "line of best fit" or the "regression line." There are various methods to calculate this line, such as the least squares method or regression analysis.
5. Equation of the line: Once you have the line of best fit, you can express it as a linear function. The equation of a linear function is typically written as y = mx + b, where y represents the dependent variable (test score), x represents the independent variable (hours studied), m represents the slope of the line, and b represents the y-intercept.
6. Interpret the coefficients: In our example, the slope (m) of the line represents the average change in test score for each additional hour of study. The y-intercept (b) is the predicted test score when the number of hours studied is zero.
By following these steps, you can use a linear function to model the relationship between the number of hours studied and test scores. Remember that the line of best fit is an approximation based on the available data, and there may be some variation or outliers in the actual relationship.