Exam (elaborations)
_2- Linear Equations and Relations
- Institution
- Modular_Arithmetic_in_the_AMC_and_AIME.
_2- Linear Equations and Relations
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Linear Equations and Relations1 AmrBoard SAT Helper 3 AmrBoard SAT Helper
er
Salma ordered a set of golf clubs and a golf bag online,
which were shipped to her house. The weight w, in
pounds, of the bag and the clubs is estimated by the
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equation w = 1.5c + 12, where c is the number of clubs
in the bag. What is the best interpretation of the number
1.5 in the equation?
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A) The estimated weight, in pounds, of 1 club
Which of the following is an equation of the line shown B) The estimated weight, in pounds, of 12 club
in the xy-plane above?
C) The estimated weight, in pounds, of the bag with no
A) y=2 clubs
B) x=2
D) The estimated weight, in pounds, of the bag with 12
H
C) y = 2x
D) x = 2y clubs
2 AmrBoard SAT Helper
AT
TM
4 AmrBoard SAT Helper
In the xy-plane, what is the slope of the line that passes
SA
through the points ( 0,0 ) and ( 4,3 ) ?
3
A system of two linear equations is graphed on the xy- A)
4
plane above. Which of following ordered pairs 4
B)
( x, y ) is the solution to the system ? 3
rd
C) 3
A) ( 1,1 ) D) 4
B) ( 1, -2 )
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C) ( 2, -1 )
D) ( 2, 1 )
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AmrBoard SAT Helper - Linear Equations and Relations 1
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, 5 AmrBoard SAT Helper 7 AmrBoard SAT Helper
A scooter rental company charges $9 for the first In the xy-plane, line M passes through the point
hour of renting a scooter and $5 for each additional 3
er
( 2,4 ) and has slope 2. Which of the following is an
hour. Which of the following functions gives the
equation of line M?
cost 𝑠(𝑡), in dollars, of renting a scooter for t hours?
3
A) S(t) = 9 t A) 𝑦 = 𝑥 + 4
2
lp
3
B) S(t) = 9 t + 6 B) 𝑦 = 𝑥 + 1
2
C) S(t) = 5t + 9 3 7
C) 𝑦 = 𝑥 −
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D) S(t) = 5 t + 4 2 2
3
D) 𝑦 = 2𝑥 +
2
6 AmrBoard SAT Helper 8 AmrBoard SAT Helper
Hours ( x ) Total cost ( y ) Zhang has run 11 races this year. The distance of each
H
1 9 race and the number of minutes it took him to
3 14 complete each race is shown in the scatterplot below.
7
9
24
29
AT
Selected values representing the total cost y, in dollars,
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to rent a bike for x hours are shown in the table above.
The relationship between x and y is linear. If the data
are graphed in the xy-plane, what is the slope of the line
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that represents this situation?
1
A)
2
rd
Which of the following is closest to the slope of a line of
B) 1 best fit for this scatterplot?
A) 2
C) 2 B) 4
C) 8
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1 D) 11
D) 2
2
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AmrBoard SAT Helper - Linear Equations and Relations 2
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, 9 AmrBoard SAT Helper 11 AmrBoard SAT Helper
In the xy-plane, what is the x-intercept of the line Which of the following is the equation of a line with x-
intercept (6, 0) and y-intercept (0, 15)?
4
er
that has a slope of and passes through the point
3 5
(A) y = x − 15
2
( 0, 8 ) ?
5
(B) y = − 2x − 15
lp
A) -8
5
(C) y = 2x +15
B) - 6
5
C) 3 (D) y = − 2x +15
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D) 8
12 AmrBoard SAT Helper
H
10 AmrBoard SAT Helper
The amount of water y, in gallons, in a reservoir x
ℎ = 70 + 5𝑚
AT
minutes after the reservoir begins to drain can be
modeled by the equation 𝑦 = 1,200 – 4𝑥.if the
A runner has a resting heart rate of 70 beats per
equation is graphed in the xy-plane which of the
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minute. For every minute he runs, his heart rate
increases by a constant number of beats per minute.
following is the best interpretation of the x-
The runner’ 3 heart rates, h, is modeled by the equation
above as a function of m minutes of running. Based on intercept?
this equation, what is the increase in heart rate for
SA
every five minutes of running?
A) The reservoir drains at the rate of 4 gallons per
minute.
B) There are 300 gallons of water in the reservoir
rd
before it begins to drain.
C) There are 1,200 gallons of water in the
reservoir before it begins to drain.
oa
D) The water will completely drain from the
reservoir 300 minutes after the reservoir
begins to drain
rB
AmrBoard SAT Helper - Linear Equations and Relations 3
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