Point-Slope and Standard Forms

Learn and apply point-slope and standard forms using equations, examples, and interpretation.

Lesson 3 of 53 parts Practice Flashcards

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Point-Slope Form

Objective: Explain and use point-slope form in an Algebra 1 problem.

A line through (x₁,y₁) with slope m can be written y−y₁=m(x−x₁); rearranging reveals other forms. Substitution should make both sides zero.

Worked examples

Try itExample 1.1: A line has slope 3 and passes through (5,31). What is its y-intercept?Show answer

16. Use y=3x+b and substitute the point to find b. The answer is 16.

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Objective: Explain and use point-slope form in an Algebra 1 problem.

A line through (x₁,y₁) with slope m can be written y−y₁=m(x−x₁); rearranging reveals other forms. Substitution should make both sides zero.

Worked examples

Try itExample 1.1: A line has slope 3 and passes through (5,31). What is its y-intercept?Show answer

16. Use y=3x+b and substitute the point to find b. The answer is 16.

Objective: Explain and use linear standard form in an Algebra 1 problem.

Ax+By=C is a linear standard form with coefficients often chosen as integers and A nonnegative by classroom convention. Set x=0 if B is nonzero.

Worked examples

Try itExample 2.1: For y=4x+26, what is the y-intercept?Show answer

26. Set x=0 and read the resulting y-value. The answer is 26.

Objective: Explain and use converting linear forms in an Algebra 1 problem.

Distribute and isolate y to convert point-slope or standard form to slope-intercept form when the line is not vertical. No, it has undefined slope.

Worked examples

Try itExample 3.1: A line has slope 2 and passes through (11,58). What is its y-intercept?Show answer

36. Use y=2x+b and substitute the point to find b. The answer is 36.

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