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Table of Contents Lines: Point-Slope Equation The point-slope equation of a nonvertical line is y – y c = m(x – x c ). Here, m is the slope and x c, y.

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Presentation on theme: "Table of Contents Lines: Point-Slope Equation The point-slope equation of a nonvertical line is y – y c = m(x – x c ). Here, m is the slope and x c, y."— Presentation transcript:

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

2 Table of Contents Slide 2 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). Lines: Point-Slope Equation First, find the slope of the line using the given points.

3 Table of Contents Slide 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)) Last, put in slope-intercept form. y – 8 = - 2x – 2 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.

4 Table of Contents 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.) Lines: Point-Slope Equation Slide 4 Next, substitute the given point, (6, 1) and slope, 2, into the point-slope equation. y – 1 = 2(x – 6) y – 1 = 2x – 12 y = 2x – 11 Last, put in slope-intercept form.

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

6 Table of Contents Lines: Point-Slope Equation

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