Practice
Rate of Change and Slope Practice
Fifty original questions using points, graphs, tables, intercepts, and applied rates.
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Question 1
Explanation
\(m=(7--1)/(2--2)=8/4=2\).
Question 2
Explanation
\(m=(-4-0)/(2--2)=-4/4=-1\).
Question 3
Explanation
\(m=(3-1)/(2--2)=2/4=0.5\).
Question 4
Explanation
\(m=(-6-2)/(2--2)=-8/4=-2\).
Question 5
Explanation
\(m=(15-3)/(2--2)=12/4=3\).
Question 6
Explanation
Using the first two rows, \(m=(7-3)/(1-(-1))=4/2=2\). The third row confirms it.
Question 7
Explanation
Using the first two rows, \(m=(7-1)/(1-(-1))=6/2=3\). The third row confirms it.
Question 8
Explanation
Using the first two rows, \(m=(7--1)/(1-(-1))=8/2=4\). The third row confirms it.
Question 9
Explanation
Using the first two rows, \(m=(7--3)/(1-(-1))=10/2=5\). The third row confirms it.
Question 10
Explanation
Using the first two rows, \(m=(7--5)/(1-(-1))=12/2=6\). The third row confirms it.
Question 11
Explanation
Average rate is \(\Delta y/\Delta x=36/2=18\) units per input unit.
Question 12
Explanation
Average rate is \(\Delta y/\Delta x=-36/3=-12\) units per input unit.
Question 13
Explanation
Average rate is \(\Delta y/\Delta x=18/4=4.5\) units per input unit.
Question 14
Explanation
Average rate is \(\Delta y/\Delta x=125/5=25\) units per input unit.
Question 15
Explanation
Average rate is \(\Delta y/\Delta x=-42/6=-7\) units per input unit.
Question 16
Explanation
Reading left to right, the line has positive slope.
Question 17
Explanation
Reading left to right, the line has negative slope.
Question 18
Explanation
Reading left to right, the line has zero slope.
Question 19
Explanation
The line is vertical, so its run is zero and division by zero makes slope undefined.
Question 20
Explanation
Reading left to right, the line has positive slope.
Question 21
Explanation
Set \(y=0\) to get \(x=4\); set \(x=0\) to get \(y=2.6666666666666665\).
Question 22
Explanation
Set \(y=0\) to get \(x=5\); set \(x=0\) to get \(y=3.75\).
Question 23
Explanation
Set \(y=0\) to get \(x=6\); set \(x=0\) to get \(y=4.8\).
Question 24
Explanation
Set \(y=0\) to get \(x=7\); set \(x=0\) to get \(y=5.833333333333333\).
Question 25
Explanation
Set \(y=0\) to get \(x=8\); set \(x=0\) to get \(y=6.857142857142857\).
Question 26
Explanation
Set \(f(x)=0\): \(1x--2=0\), so \(x=-2\). This is the x-intercept.
Question 27
Explanation
Set \(f(x)=0\): \(2x--2=0\), so \(x=-1\). This is the x-intercept.
Question 28
Explanation
Set \(f(x)=0\): \(3x-0=0\), so \(x=0\). This is the x-intercept.
Question 29
Explanation
Set \(f(x)=0\): \(4x-4=0\), so \(x=1\). This is the x-intercept.
Question 30
Explanation
Set \(f(x)=0\): \(5x-10=0\), so \(x=2\). This is the x-intercept.
Question 31
Explanation
\((k-2)/(3-(-1))=1\), so \(k-2=4\) and \(k=6\).
Question 32
Explanation
\((k-2)/(3-(-1))=2\), so \(k-2=8\) and \(k=10\).
Question 33
Explanation
\((k-2)/(3-(-1))=3\), so \(k-2=12\) and \(k=14\).
Question 34
Explanation
\((k-2)/(3-(-1))=4\), so \(k-2=16\) and \(k=18\).
Question 35
Explanation
\((k-2)/(3-(-1))=5\), so \(k-2=20\) and \(k=22\).
Question 36
Explanation
Slope is change in y over change in x, with the same subtraction order: \(6/3=2\).
Question 37
Explanation
Slope is change in y over change in x, with the same subtraction order: \(6/3=2\).
Question 38
Explanation
Slope is change in y over change in x, with the same subtraction order: \(6/3=2\).
Question 39
Explanation
Slope is change in y over change in x, with the same subtraction order: \(6/3=2\).
Question 40
Explanation
Slope is change in y over change in x, with the same subtraction order: \(6/3=2\).
Question 41
Explanation
Solve for y: \(1y=-2x+10\), so the coefficient of x is \(-2/1\).
Question 42
Explanation
Solve for y: \(2y=-3x+10\), so the coefficient of x is \(-3/2\).
Question 43
Explanation
Solve for y: \(3y=-4x+10\), so the coefficient of x is \(-4/3\).
Question 44
Explanation
Solve for y: \(4y=-5x+10\), so the coefficient of x is \(-5/4\).
Question 45
Explanation
Solve for y: \(5y=-6x+10\), so the coefficient of x is \(-6/5\).
Question 46
Explanation
\((22-30)/(5-1)=-8/4=-2\). The negative sign records a decrease.
Question 47
Explanation
\((23-35)/(6-2)=-12/4=-3\). The negative sign records a decrease.
Question 48
Explanation
\((24-40)/(7-3)=-16/4=-4\). The negative sign records a decrease.
Question 49
Explanation
\((25-45)/(8-4)=-20/4=-5\). The negative sign records a decrease.
Question 50
Explanation
\((26-50)/(9-5)=-24/4=-6\). The negative sign records a decrease.
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Questions to review
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- Question 1Slope from two pointsEasy
- Question 2Slope from two pointsEasy
- Question 3Slope from two pointsEasy
- Question 4Slope from two pointsEasy
- Question 5Slope from two pointsEasy
- Question 6Slope from tableEasy
- Question 7Slope from tableEasy
- Question 8Slope from tableEasy
- Question 9Slope from tableEasy
- Question 10Slope from tableEasy
- Question 11Average rate of changeEasy
- Question 12Average rate of changeEasy
- Question 13Average rate of changeEasy
- Question 14Average rate of changeEasy
- Question 15Average rate of changeEasy
- Question 16Slope classificationMedium
- Question 17Slope classificationMedium
- Question 18Slope classificationMedium
- Question 19Slope classificationMedium
- Question 20Slope classificationMedium
- Question 21Intercepts from standard formMedium
- Question 22Intercepts from standard formMedium
- Question 23Intercepts from standard formMedium
- Question 24Intercepts from standard formMedium
- Question 25Intercepts from standard formMedium
- Question 26Function zeroMedium
- Question 27Function zeroMedium
- Question 28Function zeroMedium
- Question 29Function zeroMedium
- Question 30Function zeroMedium
- Question 31Missing coordinate from slopeMedium
- Question 32Missing coordinate from slopeMedium
- Question 33Missing coordinate from slopeMedium
- Question 34Missing coordinate from slopeMedium
- Question 35Missing coordinate from slopeMedium
- Question 36Slope formula structureMedium
- Question 37Slope formula structureMedium
- Question 38Slope formula structureMedium
- Question 39Slope formula structureMedium
- Question 40Slope formula structureMedium
- Question 41Slope from standard formHard
- Question 42Slope from standard formHard
- Question 43Slope from standard formHard
- Question 44Slope from standard formHard
- Question 45Slope from standard formHard
- Question 46Signed average rateHard
- Question 47Signed average rateHard
- Question 48Signed average rateHard
- Question 49Signed average rateHard
- Question 50Signed average rateHard