Point-slope

Point-slope

What is it?

Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

In simple words

• Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1).
• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m

Important terms

Point-Slope: Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

What you should learn

• Define and explain point-slope.
• Apply point-slope to a focused FBISE question.
• Check the answer for correct terms, evidence, working, and units.

Examples

• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m

CORE UNDERSTANDING

Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Full school-level explanation

Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

Learn the idea, then use it:

WHAT — POINT-SLOPE

Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

HOW — Use the idea

Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.

CORE UNDERSTANDING

Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.

Remember

• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m

Examples

• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m
• POINT-SLOPE: Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Remember

• correct term
• chapter link
• clear application

Examples

• Define first
• Show the rule or evidence
• Check units, labels, and conclusion

Remember

• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m
• keep the ideas separate
• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m
• correct term

Deeper understanding

Go beyond memorising Point-slope. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

Key Points

Simple Check

How to Answer

Exam focus

Quick revision

• y - y1 = m(x - x1)
• through (x1, y1)
• gradient m
• keep the ideas separate
• Point-Slope: Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is po
• WHAT — POINT-SLOPE: Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is po

Do not merge point-slope with a neighbouring idea that uses a different definition, rule, or method.

For long answers on Point-slope: define clearly → explain the main parts → give one example → state one exam caution.