Parents and Teachers: Support Ducksters by following us on or .
Intro to Linear Equations
A linear equation is an equation that describes a straight line on a graph. You can remember this by the "line" part of the name linear equation.
Linear equations have a standard form that looks like this:
Ax + By = C
Where A, B, and C are coefficients (numbers) while x and y are variables.
You can think of the x and y variables as points on a graph.
Example linear equations:
You can plug numbers into A, B, and C of the above standard form to make linear equations:
2x + 3y = 7
x + 7y = 12
3x - y = 1
Linear Equations Represent Lines
At first it may seem strange that an equation represents a line on a graph. To make a line you need two points. Then you can draw a line through those two points.
The x and y variables in the linear equation represent the x and y coordinates on a graph. If you plug in a number for x, you can calculate the corresponding number for y. Those two numbers show a point on a graph. If you keep plugging in numbers for x and y in a linear equation, you will find that all the points together make a straight line.
Graphing a Linear Equation
In order to graph a linear equation you can put in numbers for x and y into the equation and plot the points on a graph. One way to do this is to use the "intercept" points. The intercept points are when x = 0 or y = 0. Here are some steps to follow:
You can check your answers by trying other numbers in the equation. Try x = 1. Solve for y. Then make sure that that point is on your line.
- Plug x = 0 into the equation and solve for y
- Plot the point (0,y) on the y-axis
- Plug y = 0 into the equation and solve for x
- Plot the point (x,0) on the x-axis
- Draw a straight line between the two points
Graph the linear equation: 2x + y = 2
Step 1: Plug in x = 0 and solve for y.
2 (0) + y = 2
y = 2
Step 2: Plug in y = 0 and solve for x.
2x + 0 = 2
2x = 2
x = 1
Step 3: Graph the x and y intercept points (0, 2) and (1,0)
Step 4: Draw a straight line through the two points
Step 5: Check the answer.
We will put in 2 for x and solve:
2(2) + y = 2
4 + y = 2
y = 2 - 4
Is the point (2,-2) on the line?
You can try some other points to double check as well.
Graph the linear equation x - 2y = 2
Step 1: x = 0
0 - 2y = 2
y = -1
Step 2: y = 0
x - 2(0) = 2
x = 2
Step 3: Graph the x and y points (0, -1) and (2,0)
Step 4: Draw a line through the two points
Step 5: Check your answer
Let's try x = 4
4 - 2y = 2
-2y = 2 - 4
-2y = -2
2y = 2
y = 1
Is the point (4,1) on the graph?
More Algebra Subjects
Linear Equations - Introduction
Linear Equations - Slope Forms
Order of Operations
Ratios, Fractions, and Percentages
Solving Algebra Equations with Addition and Subtraction
Solving Algebra Equations with Multiplication and Division
Back to Kids Math
Back to Kids Study