Algebra 1 You Will Learn To: Find the slope of a line. Use the rate of change to solve problems. The slope of a line is a __________________ determined by _____________________________________ on the line. This number describes how ________________ the line is. Slope is the ratio of the _______________________________________________ ( _________ ) to the ______________________________________________ ( ___________ ) as you move from one point to the other. The graph show a line that passes through (1, 3) and (4, 5). slope = = = = So, the slope of the line is Slope of a Line y xThe slope of a line is the ______________________ __________________________________________ The slope ______ of a _______________________ line through _______________________________ _________________________________________ can be found as follows. = D= Dxy m EXAMPLE: POSITIVE SLOPE Find the slope of the line that passes through the points (-1, 2) and (3, 4). Let (-1, 2) = ( ) x1, y1 and (3, 4) = ( ) x2 , y2 Now let (3, 4) = ( ) x1, y1 and (-1, 2) = ( ) x2 , y2 EXAMPLE: NEGATIVE SLOPE Find the slope of the line that passes through the points (-1, - 2) and (- 4, 1). y x ( ) x1, y1 ( ) x2 , y2 y xLet (-1, - 2) = ( ) x1, y1 and (- 4, 1) = ( ) x2 , y2 Now let (- 4, 1) = ( ) x1, y1 and (-1, - 2) = ( ) x2 , y2 EXAMPLE: ZERO SLOPE Find the slope of the line that passes through the points (1, 2) and (-1, 2). Let (1, 2) = ( ) x1, y1 and (-1, 2) = ( ) x2 , y2 Now let (-1, 2) = ( ) x1, y1 and (1, 2) = ( ) x2 , y2 EXAMPLE: UNDEFINED SLOPE Find the slope of the line that passes through the points (1, - 2) and (1, 4). y x y xLet (1, - 2) = ( ) x1, y1 and (1, 4) = ( ) x2 , y2 Now let (1, 4) = ( ) x1, y1 and (1, - 2) = ( ) x2 , y2 Classifying Lines Positive Slope Line slopes ______from ________ to _________ Negative Slope Line slopes ______from ________ to _________ Slope of 0 ________________ line Undefined Slope ________________ line EXAMPLE: Find Coordinates Given Slope y x y x y x y x y xFind the value of r so that the line through (r, 6) and (10, - 3) has a slope of 23 - . 2 12 1 x xy y m -= - Find the value of r so that the line through (6, 3) and (r, 2) has a slope of 21 . 2 12 1 x xy y m -= - RATE OF CHANGE y x y x__________________ can be used to describe a _____________________________________. The rate of change tells, on average, how a quantity is _________________________________________. The graph below shows the number of U.S. passports issued in 1991, 1995, and 1999. a) Find the rates of change for 1991 – 1995 and 1995 – 1999. b) Explain the meaning of the slope in each case. c) How are the different rates of change shown on the graph?