Rates of Change (Slope)

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Presentation transcript:

Rates of Change (Slope) Section P.2

After this lesson, you should be able to: find the slope of a line passing through two points write the equation of a line given the point and the slope sketch the graph of a linear equation in slope-intercept form write equations of lines that are parallel or perpendicular to a given line

Slope of a Line m = = = change in y change in x rise run Slope: Also, where A line has the same slope everywhere.

Equations of Lines To write the equation of a line, you need: one point the slope Remember: Equations of lines are first degree equations.

Point-Slope Equation of a Line Given the slope m passing through the point , an equation of the line can be written in the form

Example Example: Find an equation of a line that has a slope of 4 and passes through the point (-2, 3).

Examples of Horizontal and Vertical Lines Example: Find an equation of a vertical line that passes through the point (-2, 6). Example: Find an equation of a horizontal line that passes through the point (-2, 6).

Graphing Lines Using Slope-Intercept Method Example: Sketch the graph of using the slope-intercept method. m = 2 b = 1 In this case, up 2 to the right 1 m = slope b = y-intercept x y

More Examples of Lines Ex: Sketch the graph of Ex: Sketch the graph of This will be a _______________ line with a __-intercept of 3. This will be a ____________ line with an ____-intercept of -2. x y x y Note: This is not a function What is the slope of the line? What is the slope of the line?

Summary of Lines General form: Ax + By + C = 0 Vertical line: x = a Horizontal line: y = b Point-slope form: y – y1 = m(x –x1) Slope-intercept form: y = mx + b

Parallel and Perpendicular Lines Two distinct nonvertical lines are parallel iff their slopes are____________________. Two distinct nonvertical lines are perpendicular iff their slopes are _______________ _________________ of each other.

Example-Parallel Line Example: Write an equation of the line that is parallel to the line x + y = 7 and passes through the point (-3, 2).

Example-Perpendicular Line Example: Write an equation of the line that is perpendicular to the line x + y = 7 and passes through the point (-3, 2).

Another Example— Parallel and Perpendicular Lines Find the general form equation of the line that passes through and is a) parallel to b) perpendicular to

MAT 224 SPRING 2007 Homework Section P.2: pages 16- 17 #1-5 odd, 15-19 odd, 23-29 odd, 35, 37, 39, 43, 57-61 odd, 69, 71