Graphs and Forms of Linear Equations
A free College Algebra lesson from the “Graphs and Forms of Linear Equations” unit, with a worked example and practice problems including step-by-step solutions.
Linear equations can be written in different forms. Slope-intercept form shows slope and y-intercept, point-slope form uses a point and slope, and standard form can reveal intercepts.
What you'll learn
- Use slope-intercept form
- Use point-slope form
- Convert standard form to graphing information
Worked example
Problem. Write the line with slope 3 and y-intercept -2.
- Use y = mx + b.
- m = 3 and b = -2.
- The equation is y = 3x - 2.
Answer: y = 3x - 2
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. In y = -4x + 9, what is the slope?
Show solution
- m is the coefficient of x.
Answer: -4
2. In y = 2x - 7, what is the y-intercept?
Show solution
- b is the constant term.
Answer: -7
3. A line with slope 5 through (2, 1) can be written as...
Choices: y - 1 = 5(x - 2) · y - 2 = 5(x - 1) · y + 1 = 2(x - 5) · y = 5x + 1
Show solution
- Use y - y1 = m(x - x1).
Answer: y - 1 = 5(x - 2)
4. For 3x + 2y = 12, what is the y-intercept?
Show solution
- Set x = 0, then solve 2y = 12.
Answer: 6
5. What is the slope of 2x - y = 5?
Show solution
- Rewrite as y = 2x - 5.
Answer: 2
Practice this interactively with instant feedback and an AI tutor.
Practice Graphs and Forms of Linear Equations Take the free placement check