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P.2 Linear Models and Rates of Change

P.2 Linear Models and Rates of Change. Calculus is a. Celebration!!!. Slope of a Line. Find the slope of the lines passing through…. (-2,0) and (3,1) (-1,2) and (2,2) (4,-3) and (4,5). Point-slope Form of the Equation of a Line. Given a point (x 1 ,y 1 ) and slope m.

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P.2 Linear Models and Rates of Change

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  1. P.2Linear Models and Rates of Change Calculus is a Celebration!!!

  2. Slope of a Line Find the slope of the lines passing through… • (-2,0) and (3,1) • (-1,2) and (2,2) • (4,-3) and (4,5)

  3. Point-slope Form of the Equation of a Line Given a point (x1,y1) and slope m y – y1 = m(x – x1) Ex. Find an equation of the line that passes through the point (1,-2) and has a slope of 3. y – (-2) = 3(x – 1) y + 2 = 3(x – 1) 0 = 3x – y - 5

  4. Summary of Equations of Lines • General Form Ax + By + C = 0 • Vertical Line x = a • Horizontal Line y = b • Slope-intercept y = mx + b • Point-slope form y – y1 = m(x – x1) Parallel lines have slopes that are Equal. Perpendicular lines have negativereciprocal slopes.

  5. Ex. Find the equations of the lines that pass through the point (2,-1) and are a.) parallel to and b.) perpendicular to the line 2x – 3y = 5. First, solve for y and find the slope of the line. a.) m = 2/3 Use point-slope form Mult. each term by 3. 3y + 3 = 2x - 4 0 = 2x – 3y – 7 or

  6. b.) What is our slope? Use point-slope form to start. Then put in general form. Dist. Mult. By 2

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