When you work with linear equations, it's important to avoid some common mistakes. These mistakes can cause confusion and lead to wrong answers. Here are some things to watch out for:

1. Mixing Up Equation Forms: Each form of a linear equation has its own purpose. For example, the slope-intercept form ($y = mx + b$) helps you easily see the slope ($m$) and the y-intercept ($b$). On the other hand, the standard form ($Ax + By = C$) is good for finding intercepts quickly. If you switch between them the wrong way, you might make mistakes.

2. Misunderstanding Slope and Intercept: In the slope-intercept form, the slope and intercept are really important. A common mistake is reading $m$ (slope) and $b$ (intercept) wrong. For example, in the equation $y = 2x + 3$, the slope is $2$ and the y-intercept is $3$.

3. Not Rearranging Properly: When using point-slope form ($y - y_1 = m(x - x_1)$), it’s very important to rearrange the equation correctly when you change it to slope-intercept or standard form. If this isn’t done right, it could lead to a wrong graph or calculator mistake.

4. Getting Signs Wrong: Be careful with positive and negative signs; they can change the direction of the graph completely. For instance, $y = -3x + 5$ has a negative slope, which means it goes down as you move along the graph.

By keeping these mistakes in mind, you’ll get better at writing and understanding linear equations!