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Maths-

General

Easy

Question

The line graph shows the wind speed recorded every 2 hours in a town, where x is the number of hours after midnight and is the wind speed, in miles per hour (mph). What is the greatest average change in wind speed, in miles per hour per hour, between two readings shown in the graph?

The correct answer is: 5 (in miles/ hr)

HINT :- The greatest average change in wind speed in miles per hour in the graph can be determined by the slope of the line connecting the two consecutive points in the graph .
Explanation :
The greatest average change in wind speed in miles per hour in the graph can be determined by the slope of the line connecting the two consecutive points in the graph .
Step 1 : calculating all possible slopes to find the greatest average speed
So slope of line connecting the readings (0,5) and (2,9) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 end fraction right parenthesis not stretchy rightwards double arrow m 1 equals fraction numerator left parenthesis 9 minus 5 right parenthesis over denominator left parenthesis 2 minus 0 right parenthesis end fraction equals 2 space left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (2,9) and (4,4) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 2 equals fraction numerator left parenthesis 4 minus 9 right parenthesis over denominator left parenthesis 4 minus 2 right parenthesis end fraction equals negative 5 over 2 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (4,4) and (6,2) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 3 equals fraction numerator left parenthesis 2 minus 4 right parenthesis over denominator left parenthesis 6 minus 4 right parenthesis end fraction equals negative 1 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (6,2) and (8,6) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 4 equals fraction numerator left parenthesis 6 minus 2 right parenthesis over denominator left parenthesis 8 minus 6 right parenthesis end fraction equals 2 left parenthesis fraction numerator in miles over denominator hr end fraction right parenthesis$
So slope of line connecting the readings (8,6) and (10,16) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 5 equals fraction numerator left parenthesis 16 minus 6 right parenthesis over denominator left parenthesis 10 minus 8 right parenthesis end fraction equals 5 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (10,16) and (12,8) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 6 equals fraction numerator left parenthesis 8 minus 16 right parenthesis over denominator left parenthesis 12 minus 10 right parenthesis end fraction equals negative 4 left parenthesis fraction numerator space in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (12,8) and (14,12) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 7 equals fraction numerator left parenthesis 12 minus 8 right parenthesis over denominator left parenthesis 14 minus 12 right parenthesis end fraction equals 2 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So slope of line connecting the readings (14,12) and (16,10) is
m= $fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 8 equals fraction numerator left parenthesis 10 minus 12 right parenthesis over denominator left parenthesis 16 minus 14 right parenthesis end fraction equals negative 1 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis$
So the greatest average change in the wind speed is m5 = 5 ( $fraction numerator text in miles end text over denominator text hr end text end fraction$ ) in between the interval (8,6) and (10,16).

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