Scribd
Upload
15 views3 pages

? Linear Equations

A linear equation is an algebraic equation with the highest power of the variable as 1, representing a straight line on a graph. It can be expressed in one variable as ax + b = 0 or in two variables as y = mx + c, with various forms including standard form. Linear equations have real-life applications in budgeting, trend prediction, and motion calculations, and can be solved using methods like graphing, substitution, and elimination.

Uploaded by

andrie.abejo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
15 views3 pages

? Linear Equations

A linear equation is an algebraic equation with the highest power of the variable as 1, representing a straight line on a graph. It can be expressed in one variable as ax + b = 0 or in two variables as y = mx + c, with various forms including standard form. Linear equations have real-life applications in budgeting, trend prediction, and motion calculations, and can be solved using methods like graphing, substitution, and elimination.

Uploaded by

andrie.abejo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 3

🧮 Linear Equations: A Complete Guide

🔹 What is a Linear Equation?

 A linear equation is an algebraic equation in which the highest power of the variable is
1.
 It represents a straight line when graphed on a coordinate plane.
 The general form of a linear equation in one variable is:
ax + b = 0, where a and b are constants, and x is the variable.
 In two variables, it's written as:
y = mx + c, where m is the slope and c is the y-intercept.

🔹 Characteristics of Linear Equations

 The graph of a linear equation is always a straight line.


 The variables are not multiplied or divided by each other.
 The variables are not raised to any power other than 1.
 Linear equations can have one solution, no solution, or infinitely many solutions.

🔹 Types of Linear Equations

1. In One Variable

 Example:
2x - 4 = 0
→ Solution: x = 2

2. In Two Variables

 Example:
y = 3x + 5
→ This equation describes a line with a slope of 3 and a y-intercept of 5.

3. Standard Form (Ax + By = C)

 A common form for linear equations in two variables.


 Example: 2x + 3y = 6

🔹 Important Terms
 Variable: A symbol (usually x or y) that represents a number.
 Coefficient: A number multiplying the variable (e.g., 2 in 2x).
 Constant: A fixed value that does not change.
 Slope (m): Indicates the steepness of the line.
 Y-intercept (c): The point where the line crosses the y-axis.

🔹 Solving Linear Equations (One Variable)

Steps to solve:

1. Simplify both sides of the equation if necessary.


2. Move variable terms to one side.
3. Move constants to the other side.
4. Divide or multiply to isolate the variable.

Example:

 3x + 5 = 11
→ Subtract 5: 3x = 6
→ Divide by 3: x = 2

🔹 Solving Linear Equations (Two Variables)

To find solutions:

 Graphing: Plot points that satisfy the equation.


 Substitution: Replace one variable with an expression.
 Elimination: Add or subtract equations to eliminate one variable.

Example system:

 x + y = 5
 x - y = 1
→ Add: 2x = 6 → x = 3, then solve for y.

🔹 Real-Life Applications of Linear Equations

 Budgeting and financial planning (e.g., total cost = fixed cost + cost per item).
 Predicting trends in business and science.
 Calculating distance, speed, and time in motion problems.
 Converting temperature between Celsius and Fahrenheit.

🔹 Tips for Mastering Linear Equations

 Always check your solution by substituting it back into the original equation.
 Practice graphing to better understand how changes in the equation affect the line.
 Understand slope:
o Positive slope: line rises
o Negative slope: line falls
o Zero slope: horizontal line
o Undefined slope: vertical line
 Memorize common forms:
o Slope-Intercept Form: y = mx + c
o Point-Slope Form: y - y₁ = m(x - x₁)
o Standard Form: Ax + By = C

You might also like