MODELS FOR SLOPE Show all work! Name ________________________ 1. The figures show four hills labeled a, b, c and d. a b c d Which hill would be easiest to climb? a b c d Which hill would be hardest to climb? a b c d The level of climbing difficulty is related to the “steepness” of the hill. List the hills a, b, c, d in order from “least steep” to “most steep”. ____________ 2. List the segments labeled p, q, r in order from “least steep” to “most steep”. p q r ____________ 3. Compare the two figures. How are they alike? How do they differ? Can you compare their “steepness” ? 4. Summary: Consider your answers to #1-3. What properties of a figure determine its steepness? The slope of a line segment is a numerical measure of its “steepness”. The slope number indicates the amount of vertical change for each unit of horizontal change. It indicates how quickly the y values are increasing or decreasing. Slope = Slope = The slope value of this segment is a positive number. The y values increase from left to right. 5. Use the x and y coordinates of points P1 and P2 to complete the table and compute the slope of this segment. Show your work! x y P1 P2 Slope Circle the correct responses: = The slope is positive/negative . The y values are increasing/decreasing . 6(a) Use the x and y coordinates of points A and B to complete the table and compute the slopes of segments AB and CD. x y x y Slope = Slope = A B C D (b) How are the two slope values related? ____________________________________ (c) Can you predict the slopes of segments AD ______? BD ______ ? and BC______? 7. An adult is on a diet. The table and graph display the resulting weights for the first 5 weeks. week x weight y 0 174 1 172 2 170 3 168 4 166 5 164 (a) Describe any patterns you observe in the table. Describe any patterns you observe in the graph. ___________________________________ ___________________________________ (b) Draw the line connecting the data points. Compute the slope of the line you have drawn. (c) Circle: The slope is ___________ positive/negative ; the y values are increasing/decreasing . (d) What does the slope value tell you about the adult’s weight change? ____________________________________________________________________ 8. A newborn baby weighs 7 pounds at birth and gains approximately ½ pound each week. (a) Complete the table for the baby’s first 6 weeks. week x (b) Graph the ordered pairs on the grid. (c) Draw the line segment connecting the points. weight y 0 1 2 3 4 5 6 (d) Describe any patterns you observe in the table. ___________________________________ Describe any patterns you observe in the graph. ___________________________________ (e) Compute the slope of the segment. (f) Circle: The slope is positive/negative ; the y values are ____________ increasing/decreasing . (g) What does the slope value tell you about the baby’s growth? _____________________________________________________________________ (h) Can you write an equation relating the weight values y to the week values x?
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