Reteaching -1. Relating Graphs to Events

Transcription

1 - Relating Graphs to Events The graph at the right shows the outside temperature during 6 hours of one da. You can see how the temperature changed throughout the da. The temperature rose F from A.M. to 8 A.M. The temperature remained at 6 F for hours, from P.M. to P.M. The graph at the right shows a train moving between stations. The train moves slowl while leaving the station. Then it picks up speed until it reaches a cruising speed. It slows down as it approaches the net station and graduall comes to a stop. Since the graph is sketched to show relationships, the aes do not need number scales. But the aes and the parts of the graph should have labels to show what the represent. The graph at the right shows the altitude of an airplane during a flight. Use the graph for Eercises 3.. What was the airplane s altitude for most of the flight?. How long did it take the airplane to reach an altitude of, ft? 3. The third segment in the graph is not as steep as the first segment. What does this mean? Sketch and label a graph of the relationship.. You enter the freewa in our car, steadil accelerating until ou are on the freewa. Then ou turn the cruise control on and drive at a constant speed. When ou reach our eit, ou slow down as ou eit the freewa until ou stop at the stoplight. Temperature ( F) Altitude (ft) A.M. 8 A.M. P.M. P.M. 8 P.M. Time Speed 6,, 8,, Rate speeding up leaving station cruising Time slowing down approaching station Time (min) Time

2 - Functions A function describes the relationship between two variables called the input and the output. In a function, each input value has onl one output value. Function: To find output, substitute values for input + into the function equation. c output variable You can list input/output pairs in a table. + Complete the table of input/output pairs for each function.. 3. d r 3. 5 Input Input 5 Output Output c input variable Input r Use the function rule 3. Find each output. For : ( ) + 6. when. 5. when. 3( ) + 3( ) + 3 You can also show input/output pairs using function rules. Function rule: + ( ) + 6 c c input output Find when. Output d 6 () + Input Output 9 6. when when 6.

3 -3 Proportional Relationships A proportional relationship is a relationship between inputs and outputs in which the ratio of inputs and outputs is alwas the same. Gallons of Gas Cost ($) /3 /6 /3 3/9 /3 ; / /3 The ratios are all the same, so the relationship is proportional. Determine if the relationship is proportional a b m s Write the ratio of each input to its corresponding output. Then simplif. n t A pet store sells dog biscuits for $3 and 5 dog biscuits for $5. Is the relationship between the price of selling dog biscuits and 5 dog biscuits proportional? Eplain.

4 - Linear Functions A function is linear if the relationship between the changes in variables is constant A function is not linear if the relationship between the changes in variables is not constant Graph each function. Determine if the function represented in the table is linear Accelerated Grade 7 Lesson -

5 - (continued) Linear Functions Accelerated Grade 7 Lesson -

6 7-5 Understanding Slope The slope of a line is, found b using two points on the line. Find the slope of the line that passes through these two points: (, 3) and (, ). To find the change in, subtract one -coordinate from the other: (3 ( )). To find the change in, subtract one -coordinate from the other: ( ). When ou find the slope of a line, the -coordinate ou use first for the rise must belong to the same point as the -coordinate ou use first for the run. change in 3 () The slope of the line is: change in 5 5 A table of values from the graph also shows the slope. Find the slope of each line... slope 3.. change in change in change in change in Compare the change in each coordinate. change in change in 5 5 slope (, ) (, 3) slope slope

7 7-6 Graphing Linear Functions You can graph a function in the coordinate plane. To plot points for the graph, use input as -values (-ais) and output as -values (-ais). output as -values This function has the form of a linear equation and is called a linear function. To draw its graph, use slope and -intercept: = + slope = -intercept = or plot points from a table and connect them in a line. Graph each linear function T input as -values T = slope = = rise run 3

8 7-7 Comparing Functions Find the slope to compare the rate of change. Use two values from a table. Use the equation = m + b. (, ) and (, ) slope , so the function in the table has the greater rate of change. For Questions, match each linear function with its rate of change.. Austin pas a registration fee of $ plus $ for ever audiobook A. he borrows B (, 5), (, 9) C.. 3 D. 5. Which function has the greater rate of change? m b. T The slope is m, which is. 5