Interpreting the unit rate as slope :
A rate is a comparison of two quantities that have different units, such as miles and hours. A unit rate is a rate in which the second quantity in the comparison is one unit.
Example 1 :
A storm is raging on Misty Mountain. The graph shows the constant rate of change of the snow level on the mountain.
A. Find the slope of the graph using the points (1, 2) and (5, 10). Remember that the slope is the constant rate of change.
Change in y-value / Change in x-value :
= 8 / 4
B. Find the unit rate of snowfall in inches per hour. Explain your method.
2 inches per hour; Sample answer : The point (1, 2) is on the line, and represents 2 inches snowfall in 1 hour.
C. Compare the slope of the graph and the unit rate of change in the snow level. What do you notice ?
They are the same.
D. Which unique point on this graph can represent the slope of the graph and the unit rate of change in the snow level ? Explain how you found the point.
(1, 2) ; Sample answer : the unit rate is the amount of snow in 1 hour. So I found the point with an x-coordinate of 1. That point is (1, 2), which, along with another point on the graph, gives 2 as the slope.
Example 2 :
The equation y = 2.75x represents the rate, in barrels per hour, that oil is pumped from Well A. The graph represents the rate that oil is pumped from Well B. Which well pumped oil at a faster rate ?
Step 1 :
Use the equation y = 2.75x to make a table for Well A’s pumping rate, in barrels per hour.
Step 2 :
Use the table to find the slope of the graph of Well A.
Slope = Unit rate
Slope = (5.5 - 2.75) / (2 - 1)
Slope = 2.75 / 1
Slope = 2.75 barrels/hour.
Step 3 :
Use the graph to find the slope of the graph of Well B.
Slope = Unit rate
Slope = rise / run
Slope = 10 / 4
Slope = 2.5 barrels/hour.
Step 4 :
Compare the unit rates.
2.75 > 2.5
So Well A’s rate, 2.75 barrels/hour, is faster.
Describe the relationships among the slope of the graph of Well A’s rate, the equation representing Well A’s rate, and the constant of proportionality
The slope and the constant of proportionality equal the value 2.75 in the equation y = 2.75x.
After having gone through the stuff given above, we hope that the students would have understood "Interpreting the unit rate as slope".
Apart from the stuff given above, if you want to know more about "Interpreting the unit rate as slope", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions