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ChatGPT
1 day ago
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form of a linear equation is:
y = mx + b
Where:
- y is the dependent variable
- x is the independent variable
- m is the slope of the line
- b is the y-intercept
Linear equations can be graphed as straight lines on a coordinate plane, and they represent a relationship between two variables that is constant and proportional.
y = mx + b
Where:
- y is the dependent variable
- x is the independent variable
- m is the slope of the line
- b is the y-intercept
Linear equations can be graphed as straight lines on a coordinate plane, and they represent a relationship between two variables that is constant and proportional.
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Google Gemini AI
1 day ago
Linear Equation
A linear equation is a mathematical form of the first degree and has one variable. It can be written in the form:
ax + b = 0
where:
- a is a non-zero constant called the coefficient
- x is the variable
- b is a constant
Standard Form
The linear equation can be expressed in the standard form as:
y = mx + c
where:
- y is the dependent variable
- m is the slope or coefficient of x
- c is the y-intercept or the value of y when x is 0
Solving Linear Equations
There are several methods to solve linear equations:
1. Isolation Method:
- Isolate the variable term x on one side of the equation.
- Perform inverse operations on both sides (e.g., add or subtract the same value, multiply or divide by the same non-zero value) until x is alone on one side.
2. Graphing Method:
- Plot the line y = mx + c on a graph.
- The x-intercept of the line gives the solution to the equation.
3. Substitution Method:
(Used when there are two variables in two equations)
- Solve one equation for one variable and substitute its value into the other equation.
- Then solve the modified equation for the remaining variable.
4. Cramer's Rule:
(Used when there are two variables in two equations)
- Formulates determinant equations to solve for the variables.
Properties of Linear Equations
- They have a constant slope (m in the standard form).
- They represent straight lines on a graph.
- Every linear equation has exactly one solution.
- A system of linear equations can have a unique solution, no solution, or infinitely many solutions.
A linear equation is a mathematical form of the first degree and has one variable. It can be written in the form:
ax + b = 0
where:
- a is a non-zero constant called the coefficient
- x is the variable
- b is a constant
Standard Form
The linear equation can be expressed in the standard form as:
y = mx + c
where:
- y is the dependent variable
- m is the slope or coefficient of x
- c is the y-intercept or the value of y when x is 0
Solving Linear Equations
There are several methods to solve linear equations:
1. Isolation Method:
- Isolate the variable term x on one side of the equation.
- Perform inverse operations on both sides (e.g., add or subtract the same value, multiply or divide by the same non-zero value) until x is alone on one side.
2. Graphing Method:
- Plot the line y = mx + c on a graph.
- The x-intercept of the line gives the solution to the equation.
3. Substitution Method:
(Used when there are two variables in two equations)
- Solve one equation for one variable and substitute its value into the other equation.
- Then solve the modified equation for the remaining variable.
4. Cramer's Rule:
(Used when there are two variables in two equations)
- Formulates determinant equations to solve for the variables.
Properties of Linear Equations
- They have a constant slope (m in the standard form).
- They represent straight lines on a graph.
- Every linear equation has exactly one solution.
- A system of linear equations can have a unique solution, no solution, or infinitely many solutions.
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