One method for graphing a function is to find two or more points on the line, plot them, and then connect those dots with a line. To find points on the line, choose any value for x, then plug that number in the function and solve for the unknown variable y. (If you need help on this topic, please review the mini lesson: "Substitute values into an equation and Solve for a variable.")

The following video will show an example of how to do this. In this example, we find four points. It is only necessary to do two points, but doing more will help you check for mistakes.

Video Source (07:51 mins) | Transcript

Not all equations come in Slope-Intercept form, but we can still graph them. The following video will show how to graph an equation in Standard Form, where all of the variables are on the same side of the equation. It’s still a straight line. Similar to the previous video, we find two or more points to plot, then connect them to form the line.

## Additional Resources

- Khan Academy: Graphing a Linear Equation: y=2x+7 (13:09 mins; Transcript)
- Khan Academy: Graphing a Linear Equation: 5x+2y=20 (04:39 mins; Transcript)

### Practice Problems

**1. Match the equation of the line with its graph.**

a. \({\text{y}}=4{\text{x}}-3\) (

b. \({\text{y}}=-2{\text{x}}+3\) (

c. \({\text{y}}= \dfrac{1}{3}{\text{x}}\) (

3.

**2. Create a graph of the line represented by the equation.**(

\({\text{y}}=2{\text{x}}-5\)

**3. Create a graph of the line represented by the equation.**(

\({\text{y}}=\dfrac{-1}{2} {\text{x}}+2\)

**4. Graph the line represented by the equation.**(

\(3{\text{x}}+4{\text{y}}=-12\)

**5. Graph the line represented by the equation.**(

\(\dfrac{1}{3}{\text{x}}{-}{\dfrac{1}{2}}{\text{y}}=5\)

**6. Plot the y-intercept for the line:**(

\({\text{y}}=-3{\text{x}}+2\)

**7. Use the information in the previous question to answer this problem.**(

Now, choose an x-value (besides \(x=0\)) and plot the point on the line \(y=−3x+2\) that corresponds to this value. Then, use these two points to graph the line.

**8. Plot the y-intercept for the line**(

\({\text{y}} = \dfrac{1}{2}{\text{x}} - 3\)

**9. Use the information in the previous question to answer this problem.**(

Now, choose an x-value (besides \(x=0\)) and plot the point on the line \({\text{y}} = \dfrac{1}{2}{\text{x}} - 3\) that corresponds to this value. Then, use these two points to graph the line.

**10. Plot the y-intercept for the line:**(

\({\text{y}} = -\dfrac{3}{5}{\text{x}} + 1\)

**11. Use the information in the previous question to answer this problem.**(

Now, choose an x-value (besides \(x=0\)) and plot the point on the line \({\text{y}} = -\dfrac{3}{5}{\text{x}} + 1\) that corresponds to this value. Then, use these two points to graph the line.

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