2-6 Connect Proportional Relationships and Slope PDF

2-6 Connect Proportional Relationships and Slope This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Lesson Goal ✓ find the slope of a line using different strat...

2-6 Connect Proportional Relationships and Slope This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Lesson Goal ✓ find the slope of a line using different strategies. interpret a slope in context and relate it to steepness on a graph This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed. Learn Slope of a Line The term slope is used to describe the steepness of a line. Slope is the rate of change between any two points on a line. The vertical change (change in y-value) is called the rise while the horizontal change (change in x-value) is called the run. So, slope is the ratio of the rise to the run. In linear relationships, the slope is always constant. rise ← vertical change between any two points slope = run ← horizontal change between the same two points This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed. Learn Slope of a Line Slope can be positive or negative. The slope of a line that points upward, from left to right, is positive, and the slope of a line that points downward, from left to right, is negative. Positive slope Negative slope This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed. Learn Find Slope from a Graph The slope of a line can be found from a graph by finding the ratio of the rise to the run between any two points on the line. rise 3 ← vertical change between ( − 2, − 1) and (2, 2) slope = = run 4 ← horizontal change between ( − 2, − 1) and (2, 2) When reading the rise and run from a graph, a rise up is positive, a rise down is negative, a run to the right is positive, and a run to the left is negative. This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  The solution with P 130 and 131 explanation next page This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  Note : 1_ assign two point into P 130 graph ( it’s optional you can choose any two point into graph ) 2_ to find slope we need to calculate change in y over change in x P 130 the solution : The solution : 10 − 5 5 Slope = 6−3 = 3 a_ slope = = 2−1 1 6 −3 3 So the slope is 3 b_ the model is 5 feet for 3 centimeters This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  P 131 40 − 20 20 8−4 5 4 5 150 100 25 2 25 This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  The solution with P 131 and 132 explanation next page This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  P 131 P 131 The solution : The solution : Also we already have ordered pairs ( 2.1, - 4.2 ) Here we already have ordered pairs ( 0,0) And ( 2.5 , - 5 ) so we can find the slope directly And ( 2 , 4 ) and the graph is a line and passes Through the origin so I can find the slope directly − 5 − − 4.2 −5 + 4.2 Slope = = = 2.5 −2.1 0.4 4 −0 4 Slope = = =2 2 −0 2 − 0.8 = =−2 0.4 This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  P 131 The solution : 6−2 Slope = −3 − −1 4 4 = = =−2 −3 + 1 −2 This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  P 132 1 In this example Anna said car speed is we need to check if her answer 64 Correct or not a _ to find speed of the car we need to find slope 128 −64 64 𝑚𝑖𝑙𝑒𝑠 Slope = = that means the speed of the car 64 miles per hour 2 −1 1 ℎ𝑜𝑢𝑟 b _ Anna found the change in the x-coordinates over the change in the y-coordinates Note ( very important ) : We should find the change in the y -coordinates over the change in the x –coordinates When we want to find slope This material may be reproduced for licensed classroom use McGraw Hill | Slope of a Line only and may not be further reproduced or distributed.  Goal #3 Apply into Real-Life situation The solution : We already have the water level rises 11 centimeters every 5 minutes I can represent it as the ratio between rises and minutes 11 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 Represent to y 5 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 Represent to x Record the data point of (10, y ) we need to know the value of y Centimeters In 10 minutes 11 × 2 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 22 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 = the value of y equals 22 5 × 2 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 10 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 This material may be reproduced for licensed classroom use That means McGraw theof water Hill | Slope a Line rises 22 centimeters in 10 minutes only and may not be further reproduced or distributed.