Solving for k and m in f(x) = kx+m

  • Thread starter Rectifier
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In summary, the process for solving for k and m in f(x) = kx+m involves isolating the terms using algebraic operations. To check for correctness, you can substitute the values back into the equation, graph it, or use a calculator. It is possible to solve without graphing using methods like substitution or elimination. If there is no solution, it means the equation is inconsistent or represents parallel lines. Real-world applications include finding rate of change, calculating slope, and determining equations of lines.
  • #1
Rectifier
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The problem

Find k and m.

## f(x) = kx+m ##

## f(3x-2)=6x-5 ##

The attempt

## t = 3x - 2 ##

## f(t) = kt + m \\ f(3x -2) = 2(3x-2) - 1 \\ f(t) = 2t - 1 \\ f(t) = kt + m \\ k=2 \\ m=-1 ##

I am not sure if I am doing this right...
 
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  • #2
You can numerically test your work. Do it.

I am not sure if I am doing this right...
Checking your work numerically (when possible) is a good way to check your calculations even if you think you are doing it right.
 

FAQ: Solving for k and m in f(x) = kx+m

What is the process for solving for k and m in f(x) = kx+m?

The process for solving for k and m in f(x) = kx+m involves isolating the k and m terms on one side of the equation by using algebraic operations. This can include combining like terms, distributing, and factoring. Once the k and m terms are isolated, the values can be determined by solving the resulting equations.

How do I know if I have solved for k and m correctly in f(x) = kx+m?

One way to check if you have solved for k and m correctly in f(x) = kx+m is to substitute the values you have found back into the original equation. If the resulting equation is true, then you have solved for k and m correctly. You can also graph the equation and see if it matches the given graph, or use a calculator to verify the solution.

Can I solve for k and m in f(x) = kx+m without graphing?

Yes, you can solve for k and m in f(x) = kx+m without graphing. This can be done by using algebraic methods such as substitution, elimination, or the quadratic formula. These methods involve manipulating the given equation to isolate the k and m terms and solving the resulting equations.

What if f(x) = kx+m has no solution?

If f(x) = kx+m has no solution, it means that the equation does not have any values for k and m that would make the equation true for all values of x. This can happen when the given equation is inconsistent or when the equation represents parallel lines that do not intersect.

Are there any real-world applications for solving for k and m in f(x) = kx+m?

Yes, there are many real-world applications for solving for k and m in f(x) = kx+m. Some examples include finding the rate of change and y-intercept in linear relationships, calculating the slope and y-intercept in a regression line, and determining the equation of a line given two points on the line.

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