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.
Standard Form
Linear equations have a standard form that looks like this:
Ax + By = C
Where A and B are coefficients (numbers) while x and y are variables. C is a constant.
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:
- 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
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.
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