How do you create a linear model in a word problem?

Question

Ethan Adkins · Accepted Answer

To find a linear function (model), we need two pieces of information:

#{("Point: " (x_1,y_1)),("[Slope](https://tutor.hix.ai): " m):}#

So, find them from the description of the problem, then use Point-Slope Form

#y-y_1=m(x-x_1)#

to come up with the equation.

I hope that this was helpful.

Avery Alexander · Answer

undefined To create a linear model in a word problem, follow these steps:

1. Identify the variables: Determine the quantities involved in the problem and assign variables to represent them.

2. Determine the relationship: Determine how the variables are related to each other. In a linear model, this relationship will be linear, meaning that one variable varies directly with another, with a constant rate of change.

3. Write the equation: Use the formula for a linear equation, which is typically in the form $ y = mx + b $, where $ y $ represents the dependent variable, $ x $ represents the independent variable, $ m $ represents the slope of the line, and $ b $ represents the y-intercept (the value of $ y $ when $ x $ is zero).

4. Substitute values: Plug in the known values from the word problem into the equation to find the unknown values.

5. Solve: Use algebraic techniques to solve for the unknown variable(s), if necessary.

6. Interpret the solution: Once you have found the solution, interpret what it means in the context of the word problem.