Slope-Intercept Form
y = mx + b gives the slope m and y-intercept b.
About this topic
The slope-intercept form y = mx + b writes a line using its slope m and its y-intercept b, the point where it crosses the y-axis. From this equation you can graph the line quickly: plot (0, b), then use the slope to step up and across to other points.
It is the most useful form for interpreting real situations. In a taxi fare y = 2.5x + 4, the 4 is a starting fee (the value when x is 0) and 2.5 is the cost per mile, the rate of change. Reading m and b directly from the equation tells the whole story without any calculation.
To write the equation, find the slope from two points, then substitute one point to solve for b. For (0, 3) and (2, 7) the slope is 2 and the intercept is 3, so y = 2x + 3. Many graphing calculators and spreadsheet trend lines report their results in this form.
Students often forget that the equation must be solved for y before m and b can be read. In 3x + y = 6 the slope is −3, not 3. A fractional slope such as 2/3 means rise 2, run 3, and a negative slope means moving down as you go right.
Key ideas
- b is where the line crosses the y-axis
- m is the rise over run
- Quick to graph from the equation
Quick check
Use cases: where Slope-Intercept Form helps
- Homework: review the key idea behind Slope-Intercept Form before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Slope-Intercept Form without notes.
- Visual learning: play with the interactive lab to see how Slope-Intercept Form changes when you adjust its inputs.
- Teaching a friend: explain Slope-Intercept Form in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Slope-Intercept Form?
y = mx + b gives the slope m and y-intercept b.
What will I learn in Slope-Intercept Form?
b is where the line crosses the y-axis. m is the rise over run. Quick to graph from the equation.
Is Slope-Intercept Form part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Slope-Intercept Form lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Slope-Intercept Form?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.