Mathematics » Introducing Graphs » Graphing with Intercepts

# Key Concepts

## Key Concepts

• Intercepts
• The x-intercept is the point, $$\left(a,0\right)$$, where the graph crosses the x-axis. The x-intercept occurs when y is zero.
• The y-intercept is the point, $$\left(0,b\right)$$, where the graph crosses the y-axis. The y-intercept occurs when y is zero.
• The x-intercept occurs when y is zero.
• The y-intercept occurs when x is zero.
• Find the x and y intercepts from the equation of a line
• To find the x-intercept of the line, let $$y=0$$ and solve for x.
• To find the y-intercept of the line, let $$x=0$$ and solve for y.
xy
0
0
• Graph a line using the intercepts
1. Find the x- and y- intercepts of the line.
• Let $$y=0$$ and solve for x.
• Let $$x=0$$ and solve for y.
2. Find a third solution to the equation.
3. Plot the three points and then check that they line up.
4. Draw the line.
• Choose the most convenient method to graph a line
1. Determine if the equation has only one variable. Then it is a vertical or horizontal line.

$$x=a$$ is a vertical line passing through the x-axis at a.

$$y=b$$ is a vertical line passing through the y-axis at b.

2. Determine if y is isolated on one side of the equation. The graph by plotting points.

Choose any three values for x and then solve for the corresponding y- values.

3. Determine if the equation is of the form $$Ax+By=C$$, find the intercepts.

Find the x- and y- intercepts and then a third point.

## Glossary

### intercepts of a line

Each of the points at which a line crosses the x-axis and the y-axis is called an intercept of the line.