Question

1. which data set represents an increasing, linear function? (1 point)

A. (1,-2),(3,1),(5,4),(7,7)
B. (1,1) (2,0), (3,-1), (4,-2)
C.(1,-3),(3,5),(5,11) (7, 18)
D.(1, 17), (2,15), (3,11), (4, 3)

2.Which function's graph passes through the points (1, 4), (2, 9) and (3, 16)
A. y = 5x + 4
B. y = (x + 1) mini 2 on the end
C. y = (x + 3) mini 2 on the end
D. y = 7x - 5

3. suppose that after one warm-up lap around a track, you run 10 laps an hour. What is an equation that represents the total numver of laps you've run, y in terms of the number of the hours you run, t?

A. y(t) = t + 10
B. y(t) = 10 (t + 1)
C. y(t) = 10t + 1
D y(t) = t + 1

5. Which of the following s an arithmetic sequence with a common difference of 2?

A -5, -3, -1, 1, 3, 5
B. 5, 3, 1, -1, -3, -5
C. 1, 2, 4, 8, 16, 32
D 32, 16, 8, 4, 2, 1

7. Which scenario describes a situation where x varies directly with y?

A. The difference between x and y is constant
B. the sum of x and y is a constant
C. The product of x and y is constant
D. The quotient of x and y is constant

10. A line with a slope of -3 passes through ( 2,5) and (4,d). What is the value of d ?

A. -1
B. 2
C.8
D.11

11. The graph of a line passes through the point (-2,1) and has a slope of 3. What is an equation of the line

A. y = -2x + 3
B. y = 7x - 2
C. y = x - 3
D = 3x + 7

14. Which line is parallel to y = 4x - 2
A. y = 4x + 3
B. y = 2x - 4
C. y = 1/4 x + 1
D y = - 1/4 x + 5

15 which line is perpendicular to y = 2x +5
A. y = 5x+2
B. y = 2x-4
C y = 1/2 x + 1
D. y = -1/2 x+5

16. How many solutions does the following system have ?
5x - 2 = y
3x + 1 = 4y
A one solution
B. two solutions
C. infinitely many solutions
D. no solutions

19. Which system of equations has (4, 1) as its solution?

A. y = 2x-7
y = 4x

B y = 3x - 11
y = -3x + 1

C y = 5x - 19
y = 4x + 1

D. y = x - 3
y = -3x + 13

Answer 1

#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Step-by-step explanation
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.

#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.

#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.

#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.