10 Algebra 2 Questions

Question

Question 1

What is the slope of the line which passes through (4, 5) and (0, 1)?
Choose one answer.
A. undefined
B. 1
C. zero
D. 4

Question 2

Solve A = one halfp + t for p in terms of A and t.
Choose one answer.
A. p = 2(A - t)
B. p = 2A - t
C. p = A - 2t
D. p = the quantity of A minus t all over two

Question 3

y varies directly as the square of x. When x = 3, y = 18. What is the value of y when x = 4?
Choose one answer.
A. 12
B. 16
C. 24
D. 32

Question 4

What is the y-intercept of 6x - 3y = 18?
Choose one answer.
A. (0, 6)
B. (0, -6)
C. (0, 3)
D. (0, -3)

Question 5

What is the equation of a vertical line passing through (-7, 2)?
Choose one answer.
A. y = -7
B. y = 2
C. x = -7
D. x = 2

Question 6

What is the equation of the line that passes through the point (6, 1) and is perpendicular to the line y = -3x + 2
Choose one answer.
A. y = -3x + 3
B. y = -3x - 9
C. y = one thirdx - 1
D. y = one thirdx + 19

Question 7

What is the solution set of |x + 3| > 7?
Choose one answer.
A. x < -10 or x > 4
B. x < 10 or x > -4
C. x > -10 or x < 4
D. x > 10 or x < -4

Question 8

Which inequality matches the graph below?

A graph shows a dotted inverted v-shaped graph with a vertex at (2, -1). The area above the dotted graph is shaded.
Choose one answer.
A. y > |x - 2| -1
B. y > -|x - 2| -1
C. y > |x + 2| -1
D. y > -|x + 2| -1

Question 9

Choose the graph which matches the following system of equations.

3x + y = -1
2x + 3y = 6
Choose one answer.
A. A graph shows two lines intersecting in the second quadrant. One line passes through points (0, 2) and (-3, 0). The other line passes through points (-1, -2) and (1, -4).
B. A graph shows two lines intersecting in the second quadrant. One line passes through points (-3, 4) and (-3, 2). The other line passes through points (-1, 2) and ( 1, -4).
C. A graph shows two lines intersecting in the first quadrant. One line passes through points (0, 2) and (-3, 0). The other line passes through points (0, 1) and (-1, -2).
D. A graph shows two lines intersecting in the fourth quadrant. One line passes through points (0, -1) and (-1, 2). . The other line passes through points (-2, 0) and (3, 0).

Question 10

Choose the system of equations which matches the following graph.

A graph shows two lines. One passes through points (0 , 3) and (2, 2). The other line passes through points zero comma two and two comma one.
Choose one answer.
A. x + 2y = 4
3x - 6y = 18
B. x - 2y = 4
3x + 6y = 18
C. x + 2y = 4
3x + 6y = 18
D. x - 2y = 4
3x - 6y = 18

Answer 1

Answer to question 1 

 

label the points as x1 = 4, y1 = 5, x2 = 0,  y2 = 1

 

To find the slope m of the line segment joining the points, use the slope formula :

 

m = y2-y1/x2-x1 = 1-5/0-4 = -4/-4 = 1

 

So the slope of the line is 1

Answer 2

1. B
2. A
3. D
4. B
5. C
6. C
7. C
8. A
9. B (with minor changes in the answer choice (-3, 2) changes to for instance (0, 2))
10. C

 

I can explain either one of the answers on demand. However, since I personally enjoyed question 10, I'd like to go for details below.

One of the lines, say line A, passes through (0 , 3) and (2, 2)

The other, say line B, one passes through (0, 2) and (2, 1)

 

Given the information above, line A's slope is:

m_A = (y₂ - y₁) / (x₂ - x₁) >>>> m_A = (2 - 3) / (2 - 0) >>>> m_A = -1/2

Given the information above, line A's slope is:
m_B = (y₂ - y₁) / (x₂ - x₁) >>>> m_B = (1 - 2) / (2 - 0) >>>> m_B = -1/2

 

Although both slopes are equal, line's equations can be different.

Why? Having the same slope is not sufficient to say two lines are overlapped but enough to say they are parallel.

How? For this you need to find y-intercept of each line. Write down the general equation of a line.

y = m * x + b

where m stands for the slope and b is y-intercept of that particular line.

 

Thus, for line A, the equation is:

(1) y = (-1/2)x + b_A

and for line B we have:

(2) y = (-1/2)x + b_B

 

However, for finding 'b_A' and 'b_B' in each equation you need to candidate a point that passes through A and B respectively.

Solve equation (1). Plug one of (0 , 3) and (2, 2) in equation (1). I chose (0,3) where x = 0 and y = 3. So:

3 = (-1/2) * 0 + b_A >>>> b_A = 3

Solve equation (2). Plug one of (0, 2) and (2, 1) in equation (2). I chose (0,2) where x = 0 and y = 2. So:
2 = (-1/2) * 0 + b_B >>>> b_B = 2

 

Substitute b_A and b_B each in equations (1) and (2) respectively.

A: y = -x/2 + 3 >>>> x + 2y = 6

B: y = -x/2 + 2 >>>> x + 2y = 4

 

Check each answer choice and try to simplify them as much as possible.
3x + 6y = 18 >>> x + 2y = 6

x + 2y = 4

 

Let me know if you need further explanation for the rest or even this one.