Slope of a Line - Day 2 Recall, the slope, m, is a measure of the steepness of a line. slope = rise run The rise is the vertical distance between two points. The run is the horizontal distance between two points. slope = difference of ycoordinates difference of xcoordinates slope = Δy Δx Key Idea Take Note: The Greek letter "Δ" (delta) represents change, so Δy represents the difference between two yvalues. The Slope Formula If A(x1, y1) and B(x2, y2) are the coordinates of two points on a line then, slope = y2 y1 x2 x 1 Example 1: Calculate the slope of the line through the following points, using the slope formula. a) A(2, 5) and B(0, 3) m = y2 y1 x2 x1 c) P m = y2 y1 x2 x1 b) C(3, 7) and D(9, 2) m = y 2 y1 x 2 x1 ,Q d) M(4, 5) and N(4, 3) m = y2 y 1 x2 x1 Take Note: The xcoordinates are the same. There is no change in x. The line is vertical. The slope is undefined. e) X(5, 4) and Y(6, 4) m = y2 y 1 x2 x1 Take Note: The ycoordinates are the same. There is no change in y. The line is horizontal. The slope is zero. Example 3: A line has a slope A(5, 3) and B(x, 12). Calculate x. and contains the points Example 4: Given the points A(0, 1), B(3, 3) and C(9, 7), show that these points are collinear. If points are collinear, it means that they lie on the same line. Therefore, the slope calculated would be the same for each pair of points. Using Slope in Word Problems In word problems, slope represents a rate of change. Some common examples are speed (km/h), hourly wage ($/h), or taxicab fare ($/km). In word problems, it is important to be able to identify your independent and dependent variables. Recall, the independent variable is the variable whose values you choose and the dependent variable is the variable whose values you calculate. Example 5: A taxi charges $12.25 for a 15 km trip and $16.75 for a 25 km trip. a) What is the independent variable? dependent variable? b) Represent the given information as ordered pairs. c) What rate does the taxi charge per kilometre? Example 6: The LeBlanc family is driving home. They are using cruise control and their speed is constant. After 3 h, they are 350 km from home. After 5h, they are 130 km from home. a) Which variable is independent and which is dependent? b) Determine the speed at which they are travelling.
© Copyright 2018