What you will be able to do
- In y = mx + b, b is the y-intercept and m is the slope.
- A line needs two correct points, but a third point helps catch errors.
- Standard form can be graphed from intercepts or rearranged.
- Check points by substituting coordinates into the equation.
Graph from slope-intercept form
Worked example 1
Graph y = 2x - 3.
- 1.Plot the y-intercept (0, -3).
- 2.Use slope 2/1: rise 2 and run 1 to reach (1, -1).
- 3.Repeat to reach (2, 1), then draw the line.
Answer: The line passes through (0, -3), (1, -1) and (2, 1).
Check: For x = 2, y = 4 - 3 = 1.
Graph from standard form
Worked example 1
Graph 2x + 3y = 12 using intercepts.
- 1.Set y = 0: 2x = 12, so x = 6. Plot (6, 0).
- 2.Set x = 0: 3y = 12, so y = 4. Plot (0, 4).
- 3.Draw the line through both intercepts.
Answer: Intercepts are (6, 0) and (0, 4).
Check: 2(6) + 3(0) = 12 and 2(0) + 3(4) = 12.
Find slope from two points
Worked example 1
Graph the line through (-2, 1) and (2, 9).
- 1.Calculate slope: (9 - 1) / (2 - (-2)) = 8/4 = 2.
- 2.Use y = 2x + b and point (-2, 1): 1 = -4 + b, so b = 5.
- 3.Graph y = 2x + 5 using the points and intercept.
Answer: y = 2x + 5
Check: At x = 2, y = 9.
Catch common graphing errors
| Error | Symptom | Fix |
|---|---|---|
| Slope reversed | Line tilts the wrong amount | Use rise over run, not run over rise |
| Negative slope lost | Line rises left to right | Make either rise or run negative |
| Axes scale changes | Points look inconsistent | Fix: label a constant scale on each axis |
| Intercept confused | First point plotted on x-axis | b is the y-intercept in y = mx + b |
Connect graphs to functions
A graph represents all ordered pairs that make the equation true. Slope describes a constant rate of change; the y-intercept describes the output when x is zero. In a context, include units and decide whether all points on the line make sense.
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Useful answers
Frequently asked questions
How many points are needed to graph a line?
Two distinct correct points determine a line. A third point is a useful accuracy check.
What if the slope is zero?
The graph is a horizontal line. A vertical line has undefined slope and cannot be written as y = mx + b.
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Sources, scope and accuracy
The worked examples and practice questions on this page are original Cambridge Veritas learning materials, not released STAAR items. Curriculum and testing details can change; use the linked Texas Education Agency pages for current official information. Cambridge Veritas is not affiliated with or endorsed by TEA.