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Mastering Point-Slope Form Equations

Learn the origins and applications of the point-slope form equation with examples and step-by-step instructions for writing linear equations. Practice finding equations in point-slope, slope-intercept, and standard form.

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Mastering Point-Slope Form Equations

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  1. Point-Slope Form of an Equation (5.5)

  2. Where does the Point-Slope form come from?

  3. Example 1: Writing Linear Equations in Point-Slope Form Write an equation in point-slope form for the line with the given slope that contains the given point. C. A. B. y -3 = -4(x)

  4. You try it: Example 1 Write an equation in point-slope form for the line with the given slope that contains the given point. a. b. slope = 0; (3, –4) y – (–4) = 0(x – 3) y + 4 = 0(x – 3) y + 4 = 0 y = -4

  5. + 4 + 4 Example 2: Writing Linear Equations in Slope-Intercept Form Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4). Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) y – 4 = 3x + 3 Distribute 3 on the right side. Add 4 to both sides. y = 3x + 7

  6. Example 3: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – (–3) = 2(x – 2) Choose (2, –3).

  7. –3 –3 Additional Example 3 Continued We now have the following: y – (–3) = 2(x – 2) Step 3 Write the equation in slope-intercept form. y + 3 = 2(x – 2) y + 3 = 2x – 4 y = 2x – 7

  8. Additional Example 4: Using Two Points to Write an Equation Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – 1 = –4(x – 0) Choose (0, 1).

  9. + 1 +1 Additional Example 4 Continued Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9) Step 3 Write the equation in slope-intercept form. y – 1 = –4(x – 0) y – 1 = –4x y = –4x + 1

  10. Summary/Review You have now learned how to write the equation of a line in three different forms. A. Slope-Intercept B. Point-Slope C. Standard Ax + By= C y = mx + b -The term with the x must come first -A, B, and C must be Integers -A must be positive -Plug values in for m, x1 and y1 -Must be solved for “y” -Must have values in place of m and b

  11. Summary Quiz: Find the equation of the line that has a slope of 3 and goes through the point (-1, 5) in: • Point-Slope Form • Slope-Intercept Form • Standard Form y-5 = 3(x+1) y = 3x+8 3x – y = -8

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