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

  • Thread starter Thread starter Rectifier
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on solving for the constants k and m in the linear function f(x) = kx + m, specifically for the equation f(3x - 2) = 6x - 5. The solution provided indicates that k equals 2 and m equals -1, derived from substituting t = 3x - 2 into the function. The method of checking calculations numerically is emphasized as a reliable way to verify the correctness of the solution.

PREREQUISITES
  • Understanding of linear functions and their forms
  • Familiarity with variable substitution techniques
  • Basic algebraic manipulation skills
  • Knowledge of numerical verification methods
NEXT STEPS
  • Study linear function transformations and their properties
  • Learn about variable substitution in algebra
  • Explore numerical methods for verifying algebraic solutions
  • Practice solving linear equations with different coefficients
USEFUL FOR

Students learning algebra, educators teaching linear functions, and anyone interested in enhancing their problem-solving skills in mathematics.

Rectifier
Gold Member
Messages
313
Reaction score
4
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...
 
Physics news on Phys.org
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.
 

Similar threads

Solve the given equation that involves fractional exponent
  • · Replies 4 ·
Replies
4
Views
3K
Finding the domain of a composite function
  • · Replies 10 ·
Replies
10
Views
2K
To find the range of a given ##\sin## function
  • · Replies 15 ·
Replies
15
Views
2K
How Can You Solve This Modulus Equation with Square Roots and Absolute Values?
  • · Replies 1 ·
Replies
1
Views
2K
Solve the simultaneous linear congruences
  • · Replies 4 ·
Replies
4
Views
2K
Solving Plane Equation 3x + 2y -z = 4
  • · Replies 8 ·
Replies
8
Views
3K
Question about this technique for solving simultaneous equations
  • · Replies 4 ·
Replies
4
Views
2K
##f(x+y) =f(x) f(y)## and ##f(1)+f(2)=5## then find ##f(-1)=?##
  • · Replies 49 ·
2
Replies
49
Views
5K
Express ##x^3+y^3## in terms of ##m## and ##n##
  • · Replies 17 ·
Replies
17
Views
3K
Solve for ##x## in the Given Problem
  • · Replies 17 ·
Replies
17
Views
2K