Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft)
Vertical Rise of Street (ft)
Dixie Hill
60
20
Bell Hill
60
40
Liberty Hill
60
30
A. Bell Hill; it rises two-thirds foot for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
D. Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel. This means it has a steeper slope than the other hills, as it rises more vertically in relation to the horizontal distance traveled.
Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft)
Vertical Rise of Street (ft)
Dixie Hill
60
20
Bell Hill
60
40
Liberty Hill
60
30
A. Bell Hill; it rises two-thirds foot for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
D. Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel. This means it has a steeper slope than the other hills, as it rises more vertically in relation to the horizontal distance traveled.
Which hill described in the table is the steepest and why?
Street
Horizontal Distance (ft) Vertical Rise of Street (ft)
Dixie Hill 60 20
Bell Hill 60 40
Liberty Hill 60 30
A. Bell Hill; it rises two-thirds foot for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel.
C. Bell Hill; it rises 3 feet for every 2 feet of horizontal travel.
D. Liberty Hill; it rises 2 feet for every 1 foot of horizontal travel.
B. Dixie Hill; it rises 1 foot for every 3 feet of horizontal travel. This means it has a steeper slope than the other hills, as it rises more vertically in relation to the horizontal distance traveled.
Which graph represents the linear function y = start fraction 1 over 5 end fractionx – 2?
A. A line on a graph passes through the points left-parenthesis negative 5 comma negative 1 right-parenthesis left-parenthesis zero comma negative 2 right-parenthesis left-parenthesis 5 comma negative 3 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis negative 5 comma negative 3 right-parenthesis left-parenthesis zero comma negative 2 right-parenthesis left-parenthesis 5 comma negative 1 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis zero comma negative 2 right-parenthesis and left-parenthesis 1 comma 3 right-parenthesis.
D. A line on a graph passes through the points left-parenthesis negative 5 comma 1 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 5 comma 3 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis negative 5 comma negative 3 right-parenthesis, left-parenthesis zero comma negative 2 right-parenthesis, left-parenthesis 5 comma negative 1 right-parenthesis.
To see this, plug in the x-coordinates (-5, 0, 5) into the equation y = (1/5)x - 2 to find the corresponding y-coordinates:
- y = (1/5)(-5) - 2 = -1 - 2 = -3
- y = (1/5)(0) - 2 = -2
- y = (1/5)(5) - 2 = 1 - 2 = -1
These points (-5, -3), (0, -2), and (5, -1) form a straight line, which is the graph of the linear function y = (1/5)x - 2.
Which graph represents the linear function y = –5x + 2?
A. A line on a graph passes through the points left-parenthesis zero comma 2 right-parenthesis and left-parenthesis 1 comma negative 3 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis 1 comma negative 3 right-parenthesis left-parenthesis 2 comma negative 1 right-parenthesis left-parenthesis 3 comma 1 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis negative 5 comma 3 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 5 comma 1 right-parenthesis.
D. A line on a graph passes through the points left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis zero comma negative 2 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis negative 5 comma 3 right-parenthesis, left-parenthesis 0 comma 2 right-parenthesis, and left-parenthesis 5 comma -23 right-parenthesis.
To see this, plug in the x-coordinates (-5, 0, 5) into the equation y = -5x + 2 to find the corresponding y-coordinates:
- y = (-5)(-5) + 2 = 27
- y = (-5)(0) + 2 = 2
- y = (-5)(5) + 2 = -23
These points (-5, 27), (0, 2), and (5, -23) form a straight line, which is the graph of the linear function y = -5x + 2.
Which function rule represents the data in the table below?
Input (x)
1
2
3
4
5
Output (y)
9
12
15
18
21
A. y = 4 + 5x
B. y = 3 + 6x
C. y = 5 + 4x
D. y = 6 + 3x