Point-Slope Form
A free Algebra I lesson from the “Functions, Linear Relationships, and Rate of Change” unit, with a worked example and practice problems including step-by-step solutions.
Point-slope form uses a known point and a slope to write the equation of a line: y - y1 = m(x - x1). It is especially useful when you know a point on the line but do not immediately know the y-intercept. The point gives the anchor, and the slope tells how the line moves from that anchor. When practicing, substitute the given point for x1 and y1, and substitute the slope for m. Be careful with signs: subtracting a negative coordinate becomes addition. A common mistake is switching x1 and y1 or losing the negative sign inside the parentheses.
What you'll learn
- Use y - y1 = m(x - x1)
- Write a line from a point and slope
- Convert point-slope form to slope-intercept form
Worked example
Problem. Write a line with slope 3 through (2, 5).
- Use y - y1 = m(x - x1).
- Substitute m = 3, x1 = 2, and y1 = 5.
- The equation is y - 5 = 3(x - 2).
- Connect the result back to Point-Slope Form so the method and meaning are both clear.
Answer: y - 5 = 3(x - 2)
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Which is point-slope form?
Choices: y - 4 = 2(x - 1) · y = 2x + 4 · 2x + y = 4 · x = 4
Show solution
- Point-slope form shows y - y1 and x - x1.
Answer: y - 4 = 2(x - 1)
2. Write a line with slope 2 through (3, 7).
Choices: y - 7 = 2(x - 3) · y - 3 = 2(x - 7) · y = 2x + 7 · y + 7 = 2(x + 3)
Show solution
- Use x1 = 3 and y1 = 7.
Answer: y - 7 = 2(x - 3)
3. In y - 5 = 4(x - 2), what is the slope?
Show solution
- The number multiplying the parentheses is m.
Answer: 4
4. Write a line with slope -1 through (4, 6).
Choices: y - 6 = -1(x - 4) · y - 4 = -1(x - 6) · y = -x + 6 · y + 6 = -1(x + 4)
Show solution
- Substitute m = -1, x1 = 4, y1 = 6.
Answer: y - 6 = -1(x - 4)
5. Write a line with slope 3 through (-2, 5).
Choices: y - 5 = 3(x + 2) · y + 5 = 3(x - 2) · y - 2 = 3(x + 5) · y = 3x - 2
Show solution
- x - (-2) becomes x + 2.
Answer: y - 5 = 3(x + 2)
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