Why should we learn this? One realworld connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY


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1 Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the intercept. One realworld connection is to find the rate of change in an airplane s altitude. VOCABULARY Rate a comparison of two quantities measured in different units Rate of change allows ou to see the relationship between two changing quantities RATE OF CHANGE FORMULA: change in dependent variable change in independent variable For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven Miles Fee 0 $ rate of change $42 $4 $66 change in cost change in number of miles Cost depends on the number of miles. The rate of change for each pair of consecutive mileage amounts is $12 per 0 miles. The rate of change is the same for all the data. Below is a graph of the distance traveled b a motorccle from its starting point. Find the rate of change. Eplain what this rate of change means. Choose two points On the graph (0,0) and (20, 400) rate of change Using the points (0,0) and (20, 400), find the rate of change. vertical change horizontal change change in distance change in time Use two points. Divide the vertical change b the horizontal change. Simplif. The rate of change is 20 m/s. The motorccle is traveling 20 meters each second. 1
2 More Vocabular SLOPE  vertical change horizontal change a. Find the slope of each line. slope rise run A.K.A. rise over run RISE RUN The slope of the line is rise over run b. Find the slope of the line. slope rise run ( 2) The slope of the line is 2. For positive slope, rise up and run right or move down and to the left. For negative slope, move down and to the right or up and to the left. Finding slope when given a graph of a line. 1. Locate two points on the line. 2. Count straight up or down from one point until ou re even with the other point. (This is our rise.) 3. Count across left or right until ou get to the second point. (This is our run.) 4. Simplif this fraction, if needed. REMEMBER If a line SLANTS UPWARD from left to right, it has a POSITIVE slope. / If a line SLANTS DOWNWARD from left to right, it has a NEGATIVE slope. \ 2
3 FORMULA Find the slope of the line through E(3, 2) and F( 2, 1). SLOPE FORMULA (where 2 1 does not equal 0.) Smbol for slope m. slope ( 2) 2 3 The slope of EF is 1. Substitute ( 2, 1) for ( 2, 2 ) and (3, 2) for ( 1, 1 ). Simplif. Find the slope of the line through each pair of points. a) (2,) and (4,7) c) (a,b) & (c,d) b) (1,4) & (3,2) Find the slope of the line through each pair of points. SOLUTION: Use the Slope formula. a) (2,) and (4,7) c) (a,b) & (c,d) 7 2 d b m 1 m c a b) (1,4) & (3,2) m a. Find the slope of each line. slope ( 4) 0 0 Substitute (1, 2) for ( 2, 2 ) and ( 4, 2) for ( 1, 1 ). Simplif. The slope of the horizontal line is 0. b. Find the slope of the line. slope ( 4) Substitute (2, 1) for ( 2, 2 ) and (2, 4) for ( 1, 1 ). Simplif. Division b zero is undefined. The slope of the vertical line in undefined. 3
4 Special Lines The slope of a horizontal line is zero. Equation is b. (No in equation.) The slope of a vertical line is undefined. Equation is a. (No in equation.) 2 Find the slope Since there is no in the equation, this is a horizontal line. The slope of a horizontal is zero. So m 0. Find the slope. Solution 3 Since there is no in the equation, this is a vertical line. The slope of a vertical line is undefined. So m undefined. Graphing a Line using the intercept and Slope Reminder: The intercept is the point where a line crosses the ais. STEPS 1. Plot the intercept. (referred to as b ) 2. Use the slope and move rise/run to plot at least two more points. Eample  Graph the line given the slope and intercept. Eample  Graph the line given the slope and intercept. intercept 3, m 1/2 intercept 3, m 1/ Plot the intercept, (0,3). m 1/2 and rise/run to   4
5 Eample  Graph the line given the slope and intercept. intercept 2, m 2/3 Eample  Graph the line given the slope and intercept. intercept 2, m 2/ Plot the intercept, (0,2). m 2/3 and rise/run to   Eample  Graph the line given the slope and intercept. Eample  Graph the line given the slope and intercept. intercept 0, m 1 intercept 0, m Plot the intercept, (0,0). m 1/1 and rise/run to SUMMARY The slope of a line represents the rate of change in the and values. The slope formula is
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