1.14.1 Using Point-Slope Form to Write the Equation of a Line

Algebra 11.14.1 Using Point-Slope Form to Write the Equation of a Line

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Warm Up

Your teacher will assign you one pair of the points shown.

Points for Line A: $(- 1, 5)$ and $(1, 1)$

Points for Line B: $(- 1, - 1)$ and $(1, - 5)$

Use your assigned points to find the following:

Find the slope of the line.

Compare your answer:

Line A: slope: $m = \frac{1 - 5}{1 - (- 1)} = - 2$

Line B: slope: $m = \frac{- 5 - (- 1)}{1 - (- 1)} = - 2$

Remember to use the slope formula to find the slope: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

Write the equation of the line in slope-intercept form.

Compare your answer:

Line A: equation $y = - 2 x + 3$

Line B: equation $y = - 2 x - 3$

Remember to use the point-slope form for the equation of the line to write the equation: $y - y_{1} = m_{1} (x - x_{1})$ . Write the equation in slope-intercept form $y = m x + b$ , where the slope is $m$ and the $y$ -intercept is $b$ .

Compare your equation to your partner’s equation. What were some things that were the same? What were some things that were different

Compare your answer:

Your answer may vary, but here are some samples.

Both lines have a negative slope.
Both lines have the same slope.
The $y$ -intercepts are different.
The $y$ -intercepts have opposite signs.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/1-14-1-using-point-slope-form-to-write-the-equation-of-a-line

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