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Section 3.3

Section 3.3. The Equation of a Line. Writing the Equation of a Line. Slope – Intercept form: y = mx + b Use when you are given the slope and (0, b) or if you are given the graph of the line. Point-Slope form: y – y 1 = m(x – x 1 )

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Section 3.3

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  1. Section 3.3 The Equation of a Line

  2. Writing the Equation of a Line • Slope – Intercept form: y = mx + b • Use when you are given the slope and (0, b) or if you are given the graph of the line. • Point-Slope form: y – y1 = m(x – x1) • Use when you are given the slope and (x, y) or if you are given 2 ordered pairs. • Don’t leave your answer in the form, check the directions to see what’s required.

  3. Ex: Write the equation of the line in slope-intercept form given: • m = - ½ : (0, -4) • m = 2; (4, -2) • (-3,2) and (5, 7)

  4. Standard Form: Ax + By = C Note: A, B, and C are integers, and A > 0 To write an equation in this form: • Rearrange so that the x and y terms are on the left and the constant is on the right. • If needed, multiply everything by the LCD to clear any fractions. • If needed, multiply everything by -1 so the coefficient of x is positive.

  5. Ex: write the equation in both slope-intercept and standard forms given: • 1. (1, 3) and (-2, -9) • 2. (-5, -2) and (6, -4)

  6. Parallel and Perpendicular Lines • Parallel lines have equal slopes. Symbol: || • Perpendicular lines have opposite reciprocal slopes. Symbol: | Ex: are the 2 lines ||, | , or neither? 6x – 2y = 7 x + 3y = -5

  7. Write the equation of the line that passes through the given point and is parallel to the given equation: (-1, 1); y = -3x + 1 Write the equation of the line that passes through the given point and is perpendicular to the given equation: (2, 8); x + 2y = 9

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