Point-Slope Form
y − y₁ = m(x − x₁) builds a line from a point and slope.
About this topic
When you know the slope and any single point on a line, point-slope form y − y₁ = m(x − x₁) gives its equation directly. It comes straight from the definition of slope: the slope between any point (x, y) and the known point (x₁, y₁) must equal m.
The form is handy when the y-intercept is not given. Suppose a line has slope 3 and passes through (2, 5). Substituting gives y − 5 = 3(x − 2), which you can leave as is or expand into y = 3x − 1. The same method works when you are given two points: first compute the slope, then use either point.
In practice it is the quickest way to build a linear model from data, such as a plant measured at 10 cm on day 2 and growing 1.5 cm per day: y − 10 = 1.5(x − 2). It is also the starting point for tangent line equations in later calculus courses.
Watch the signs. The subtraction in the parentheses means that a point like (−4, 1) becomes y − 1 = m(x + 4). Another common slip is putting the coordinates in the wrong places, so remember that y goes with y and x goes with x.
Key ideas
- Use any point on the line
- Convert to slope-intercept by distributing
- Great when intercept is unknown
Quick check
Use cases: where Point-Slope Form helps
- Homework: review the key idea behind Point-Slope Form before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Point-Slope Form without notes.
- Visual learning: play with the interactive lab to see how Point-Slope Form changes when you adjust its inputs.
- Teaching a friend: explain Point-Slope 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 Point-Slope Form?
y − y₁ = m(x − x₁) builds a line from a point and slope.
What will I learn in Point-Slope Form?
Use any point on the line. Convert to slope-intercept by distributing. Great when intercept is unknown.
Is Point-Slope 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 Point-Slope 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 Point-Slope 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.