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Intermediate 𝑥 Algebra Topic 20 of 100

Point-Slope Form

Line through (x₁,y₁) with slope m.

Key idea

Line through (x₁,y₁) with slope m.

In depth

y − y₁ = m(x − x₁) builds the equation of a line from one known point and the slope. It comes directly from the definition of slope applied to a general point (x, y).

Worked example

Slope 3 through (2, 5): y − 5 = 3(x − 2), which simplifies to y = 3x − 1.

Formula

y − y₁ = m(x − x₁)

Real-world uses

Common mistake

Using the wrong signs: the point (2, 5) appears as x − 2, not x + 2.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Point-Slope Form?

Line through (x₁,y₁) with slope m. It is a topic at the intermediate level in Algebra.

What is the formula for Point-Slope Form?

The key formula is y − y₁ = m(x − x₁).

Where is Point-Slope Form used in real life?

Real-world examples: Writing the equation of a line from one known point and its slope in engineering and design.

What should I learn before Point-Slope Form?

Make sure you are comfortable with Slope-Intercept Form, the previous topic in Algebra.

What is a common mistake with Point-Slope Form?

Using the wrong signs: the point (2, 5) appears as x − 2, not x + 2.

How can I practise Point-Slope Form?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Point-Slope Form?

Move on to Standard Form of a Line next.

Related intermediate topics in Algebra