6 Questions
What is the general form of a linear equation in two variables?
ax + by = c
What is the purpose of the slope-intercept form of a linear equation?
To determine the slope of a line
What is the standard form of a linear equation?
Ax + By = C
What is the purpose of the addition and subtraction properties in solving linear equations?
To isolate the variable on one side of the equation
What is the y-intercept of a line in the slope-intercept form?
The point where the line crosses the y-axis
What is the definition of a linear equation?
An equation with a variable of degree 1
Study Notes
Linear Equations
Definition
- A linear equation is an equation in which the highest power of the variable(s) is 1.
- General form: ax + by = c, where a, b, and c are constants, and x and y are variables.
Types of Linear Equations
- Simple Linear Equation: An equation with only one variable, e.g., 2x = 5.
- Linear Equation in Two Variables: An equation with two variables, e.g., 2x + 3y = 7.
Slope-Intercept Form
-
Slope-Intercept Form: y = mx + b, where:
- m is the slope (a measure of how steep the line is).
- b is the y-intercept (the point where the line crosses the y-axis).
Standard Form
-
Standard Form: Ax + By = C, where:
- A, B, and C are integers.
- A is non-negative.
- There are no fractions or decimals.
Graphing Linear Equations
- X-Intercept: The point where the line crosses the x-axis.
- Y-Intercept: The point where the line crosses the y-axis.
- Slope: The steepness of the line, which can be positive, negative, or zero.
Solving Linear Equations
- Addition and Subtraction Properties: Add or subtract the same value to both sides of the equation to isolate the variable.
- Multiplication and Division Properties: Multiply or divide both sides of the equation by a non-zero value to isolate the variable.
Linear Equations
Definition
- Linear equations have the highest power of variables as 1.
- General form: ax + by = c, where a, b, and c are constants, and x and y are variables.
Types of Linear Equations
- Simple Linear Equation: one variable, e.g., 2x = 5.
- Linear Equation in Two Variables: two variables, e.g., 2x + 3y = 7.
Slope-Intercept Form
- Slope-Intercept Form: y = mx + b, where:
- m is the slope (steepness of the line).
- b is the y-intercept (point where the line crosses the y-axis).
Standard Form
- Standard Form: Ax + By = C, where:
- A, B, and C are integers.
- A is non-negative.
- No fractions or decimals.
Graphing Linear Equations
- X-Intercept: point where the line crosses the x-axis.
- Y-Intercept: point where the line crosses the y-axis.
- Slope: steepness of the line (positive, negative, or zero).
Solving Linear Equations
- Addition and Subtraction Properties: add or subtract the same value to both sides to isolate the variable.
- Multiplication and Division Properties: multiply or divide both sides by a non-zero value to isolate the variable.
Learn about linear equations, their definition, types, and slope-intercept form. Understand the general form of linear equations and how to work with them.
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