When you graph linear equations, some common mistakes can make your graphs confusing. Here’s a simple list of things to watch out for:

1. Mixing Up the Slope and Y-Intercept

In the slope-intercept form $y = mx + b$, $m$ stands for the slope and $b$ stands for the y-intercept. Sometimes it can be tricky.

For example, in the equation $y = -2x + 3$, the slope is $-2$. This means for every time you go to the right 1 unit, you go down 2 units. The y-intercept is $3$, which is where the line crosses the y-axis. If you confuse these numbers, your graph won't match the equation.

2. Missing the Y-Intercept

Many students remember the slope but forget to start at the y-intercept! Always start your graph where the line crosses the y-axis. In our example, this would be at the point $(0, 3)$.

3. Using a Wobbly Scale

When you draw the axes, it’s important to keep the scale the same. If you mark the x-axis in intervals of 1, stick to that for everything. If your scale is inconsistent, your line may look steeper or flatter than it really is.

4. Not Plotting Enough Points

Some students just plot the y-intercept and one other point using the slope. It’s better to plot at least two points, or even three, to get it right. For example, starting from $(0, 3)$ and moving with a slope of $-2$, you would also mark points like $(1, 1)$ and $(2, -1)$.

5. Forgetting to Label Things

Always label your axes and the important points on your graph. This makes it easier to understand and talk about your graph later. For example, label the point $(1, 1)$ clearly.

If you avoid these mistakes, graphing linear equations will be easier and more fun! Happy graphing!