Home > Pre-Algebra > Linear Equations > One Step Linear Equations

## One Step Linear Equations

#### Introduction

A linear equation is an equation describing a line on a graph. The usual format for a linear equation is y=mx+b (this is called the slope-intercept format). m is the slope of the line (how steeply it goes up or down) and b is the y-intercept (which is where the line crosses the y-axis - also the point at which x=0).

To solve one-step linear equations, you just have to combine the like terms.

## Lesson

For this type of linear equation, we'll be focusing on the slope-intercept format (y=mx+b).

That means we need to get y on one side of the equation (not 2y, or -y, but exactly y), and the x variable and the number on the right-hand side of the equation.

An example of a slope-intercept linear equation is:

$y=2x+1$

To 'solve' a linear equation, we don't find the value for x and y (and we can't, unless we're given another line to combine it with), but instead, we have to put the equation in this format.

If we are given the equation:

$7y - 6y = 2x + 7$

Since the right-hand side of the equation is complete, we just need to combine the like terms on the left-hand side. To do that, we do 7y-6y, which gives the answer y.

Therefore, the solution is:

$y=2x+7$

We can solve the equation in one step as long as there is only one set of like terms to combine.

## Examples

$-1 = x + 8$
 $-1$ $=$ $x + 8$ $-8$ $=$ $-8$ $-9$ $=$ $x$
Lily starts with 6 pears, and after Madison gives Lily a few more pears, Lily has 11 pears. How many pears did Madison give Lily?
Create equation for problem
 $x + 6$ $=$ $11$ $-6$ $=$ $-6$ $x$ $=$ $5$