Slope, Mon., Jan. 9th, 7th Grade

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Presentation transcript:

Slope, Mon., Jan. 9th, 7th Grade GLE 0706.3.6 Conceptualize the meanings of slope using various interpretations, representations, and contexts. Assessments: Understand that the graph of a linear function f is the set of points on a line representing the ordered pairs (x, f(x)). SPI 0706.3.4 Interpret the slope of a line as a unit rate given the graph of a proportional relationship. Essential Question: How do we graph data, find slope and explain what slope means.

Graph the data; Find the slope; Explain what the slope represents. 1 Graph the data; Find the slope; Explain what the slope represents. 1. Envelopes The table shows the number of envelopes stuffed for various times. To graph the data, use the graph next to problem 1; go to the 5 line at the bottom, from there go up to 30 (the second line); place a dot where the 5 and 30 intersect. Slope formula: slope= y2-y1/x2-x1 : Pick any 2 ordered pairs for ex. (5, 30) and (10, 60); Plug in those numbers into the slope formula 60-30/10-5= 30/5=6 The slope shows how steep the line is. It is the ratio of the vertical change to the horizontal change in the straight line. Time (min) X 5 10 15 20 Envelopes Stuffed Y 30 60 90 120

Yards (X) 1 (X1) 2 (X2) Feet (Y) 3 (Y1) 6 (Y2) 2. Measurement There are 3 feet for every yard Make a chart similar to the one in #1. It should have at least two ordered pairs or sets of numbers for X and Y. For example, the first ordered pair would be (1, 3) where 1 is the yard and 3 is the feet. The second ordered pair could be (2, 6) where 2 is the yards and 6 represents the number of feet. Graph as you did in #1 Find the slope using the slope formula as you did in #1. Slope = Y2-Y1/X2-X1; or Explain what slope represents as I did in #1. Yards (X) 1 (X1) 2 (X2) Feet (Y) 3 (Y1) 6 (Y2)

3. Use the graph that shows the number of laps completed over time 3. Use the graph that shows the number of laps completed over time. Find the slope of the line. a) Time in minutes is X with 10 as X1 and 20 or 30 as X2; b) Number of laps is Y with 5 as Y1 and 10 or 15 as Y2. c) Decide which ordered pairs you want to use The easiest to use is (10,5) and (20, 10). d) Plug the numbers into the formula for Slope which is Slope = Y2-Y1/X2-X1. Which line is the steepest? Explain using the slopes of lines l, m, and n. Slope = Y2-Y1/ X2-X1 a. Slope for l= 2- 1/ 2-0= b. Slope for m= 2- -4/2-0= c. Slope for n= 3- -3/ 0- 3=

Page 108, 1-4 Go-Karts The graph shows the average speed of two go-karts in a race. What does the point (2,20) represent on the graph? If the point was (1,10), you could say that 1 is for 1 hour; 10 is for 10 miles, so the go-kart Y was traveling 10 miles per hour at the beginning of the race. Be sure to include which go-kart the point is referring to. What does the point (1,12) represent on the graph? Follow the clues above. What does the slope of each line represent? Look in your notes to find what slope represents. Which car is traveling faster? Which car goes more distance in the same amount of time as the other car?

2. Skateboarding The line represents the length and height of a skateboard ramp. Find the slope of the ramp. Put two points anyplace on the line. Write down the ordered pairs of the points you selected. Decide what numbers are Y2, Y1, X2 and X1. Then plug them into the slope formula, Y2-Y1/ X2-X1

3. Raisins The table shows the number of packages of raisins per box. Graph the data. Hint: Boxes are X; Packages are Y Find the slope of the line. Write the formula first, then plug in the numbers for any two ordered pairs. Explain what the slope represents. Look in your notes. 4. Resort The Snells can spend 4 nights at a resort for $500 or 6 nights at the same resort for $750. Graph the data. Hint: number of nights is the input or X; cost is the output or Y Then find the slope. Write the formula first, then plug in the numbers for these two ordered pairs.