The slope describes the rate and direction of change.
Free Interactive Algebra Tool
Point-Slope Form Practice
Learn how to use y − y₁ = m(x − x₁) to write linear equations from a point and slope, work from two points, and convert equations between linear forms.
Start practicingNeed Help With Point-Slope Form?
Review y − y₁ = m(x − x₁), how to identify the slope and point, handle negative coordinates, write equations from two points, and convert to slope-intercept form.
Read the Point-Slope Form Guide
Practice Mode
Choose how you want to practice point-slope form.
Problem 1 of 10
10%
Current Problem
Identify the slope and point used in the equation.
Identify Parts
Beginner
Current Problem
y − 4 = 3(x + 2)
1
Find m
2
Find Point
3
Interpret
Step 1
Identify the slope
Compare the equation with y − y₁ = m(x − x₁).
y − 4 = 3(x + 2)
Step 1
Substitute the slope
Use the given slope and point in y − y₁ = m(x − x₁).
Slope
m = 3
Point
(−2, 4)
Step 1
Find the slope
Use the two points to calculate rise over run.
Point 1
(1, 2)
Point 2
(3, 6)
Step 1
Distribute the slope
Begin converting point-slope form into slope-intercept form.
y − 2 = 3(x − 4)
Compare the equation with y − y₁ = m(x − x₁).
Hint
Match each part to y − y₁ = m(x − x₁).
Point-Slope Form Reference
y − y₁ = m(x − x₁)
Point-slope form describes a line using one known point and the line's slope.
The coordinates of a point on the line are substituted for x₁ and y₁.
Subtracting a negative coordinate turns into addition.
The same double-negative rule applies on the left side of the equation.
Find the slope first, then use either original point in point-slope form.
Distribute the slope and then solve the equation for y.
Problem Complete
y − 4 = 3(x + 2)
The equation has slope 3 and passes through the point (−2, 4).
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Practice Round Complete
Great work!
You completed all 10 point-slope form problems.
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Start with a known point
Point-slope form uses the coordinates of any known point on the line, not necessarily the y-intercept.
Use the slope
The value of m controls the line's rate of change just as it does in slope-intercept form.
Convert between forms
Point-slope form and slope-intercept form can describe the exact same line in different ways.
Example
Write the line with slope 3 through (−2, 4)
Begin with the point-slope formula y − y₁ = m(x − x₁).
y − 4 = 3(x + 2)
1
Substitute the slope
m = 3
2
Substitute the point
x₁ = −2 and y₁ = 4
3
Simplify the double negative
x − (−2) becomes x + 2
The plus sign inside the parentheses does not mean x₁ is positive. Because the formula contains x − x₁, substituting x₁ = −2 creates x − (−2) = x + 2.
Practice Point-Slope Form Step by Step
Point-slope form is a useful way to write a linear equation when you know the slope of a line and one point that lies on it. The formula is y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is a point on the line.
This interactive point-slope form practice tool emphasizes the meaning of every part of the formula instead of asking students to memorize a substitution pattern.
Identify the Parts of Point-Slope Form
Students practice reading an equation and identifying the slope m and the point (x₁, y₁). Special attention is given to equations containing addition, because x + 3 actually corresponds to x₁ = −3.
Write Point-Slope Form From a Point and Slope
When a slope and one point are given, substitute the slope for m and the coordinates for x₁ and y₁. Simplifying double negatives correctly is one of the most important skills in this process.
Write Point-Slope Form From Two Points
If two points are given, first calculate the slope using the slope formula. Then choose either original point and substitute it into point-slope form.
Convert Point-Slope Form to Slope-Intercept Form
Point-slope equations can be converted to y = mx + b by distributing the slope and then isolating y. Practicing both forms helps students see that different equations can represent the same line.
Three Difficulty Levels
Beginner problems use simple integer slopes and coordinates. Intermediate practice introduces negative coordinates, fractional slopes, and more sign changes. Advanced problems combine fractions, two-point problems, and multi-step conversions.
Build Stronger Linear Equation Skills
Understanding point-slope form connects slope, coordinate geometry, slope-intercept form, graphing linear equations, parallel and perpendicular lines, and writing equations from real-world information.