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Lines: Point-Slope Equation

Example 1: Write the slope-intercept equation of the line that contains the point (- 2, 5) and has slope . Lines: Point-Slope Equation. The point-slope equation of a nonvertical line is y – y c = m ( x – x c ).

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Lines: Point-Slope Equation

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  1. Example 1: Write the slope-intercept equation of the line that contains the point (- 2, 5) and has slope Lines: Point-Slope Equation The point-slope equation of a nonvertical line is y – yc = m(x – xc). Here, m is the slope and xc,yc are the x- and y-coordinates of a point on the line. First, substitute the given point and slope into the point-slope equation.

  2. Lines: Point-Slope Equation Next, put in slope-intercept form. Example 2: Write the slope-intercept equation of the line that contains the points (- 1, 8) and (4, - 2). First, find the slope of the line using the given points. Slide 2

  3. Lines: Point-Slope Equation Next, substitute either given point (say, (- 1, 8)) and the slope, - 2, into the point-slope equation. y – 8 = - 2(x– (- 1)) y – 8 = - 2x– 2 Last, put in slope-intercept form. y = - 2x+ 6 Example 3: Write the slope-intercept equation of the line that contains the point (6, 1) and is parallel to the line y = 2x + 9. First, note that the given line is in slope-intercept form, y = mx + b, so its slope is 2. Since parallel lines have the same slope, the slope of the line you need to find is 2. Slide 3

  4. Lines: Point-Slope Equation Next, substitute the given point, (6, 1) and slope, 2, into the point-slope equation. y – 1 = 2(x– 6) y – 1 = 2x– 12 Last, put in slope-intercept form. y = 2x– 11 Notes: The point-slope equation can be used for any nonvertical line. Recall that the equation of a vertical line may have the form x = real number. A line containing the points (2, - 4) and (2, 1) is vertical (plot the points to see this) so its equation is x = 2. (Every point on the line has x-coordinate of two.) Slide 4

  5. The equation is Try: Write the slope-intercept equation of the line that contains the point (1, - 2) and is perpendicular to the line Lines: Point-Slope Equation Try: Write the slope-intercept equation of the line that contains the points (3, - 7) and (7, 3). The equation is y = - 4x + 2. Slide 5

  6. Lines: Point-Slope Equation END OF PRESENTATION Click to rerun the slideshow.

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