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1. Name the quadrant, if any, in which each point is located.
(a) (-3, 6)
(b) (7, -5)
Solution:
(a) (-3, 6) --------- II Quadrant.
(b) (7, -5) --------- IV Quadrant.
2. Complete the table for the given equation and graph the equation;
x + 2y = 5
Solution:
x + 2y = 5
Put the value of x = 0 in the equation x + 2y = 5
0 + 2y = 5
2y = 5
2y/2 = 5/2
y = 5/2
(0, 5/2)
Put the value of y = 0,
x + 2 × 0 = 5
x = 5
(5, 0)
Put the value of x = 2,
2 + 2y = 5
2 – 2 + 2y = 5 - 2
2y = 3
2y/2 = 3/2
y = 3/2
(2, 3/2)
Put the value of y = 2,
x + 2 × 2 = 5
x + 4 = 5
x + 4 – 4 = 5 – 4
x = 1
(1, 2)
3. Complete the table for the given equation and graph the equation;
6x-5y=30
Solution:
6x-5y=30
Put the value of x = 0 in the equation 6x - 5y = 30.
6 × 0 - 5y = 30
-5y = 30
-5y/-5 = 30/-5
y = -6
(0, -6)
Put the value of y = 0,
6x - 5 × 0 = 30
6x = 30
6x/6 = 30/6
x = 5
(5, 0)
Put the value of x = 3,
6 × 3 - 5y = 30
18 - 5y = 30
18 – 18 – 5y = 30 – 18
-5y = 12
-5y/-5 = 12/-5
y= -12/5
(3, -12/5)
Put the value of y = -2,
6x – 5(-2) = 30
6x + 10 = 30
6x + 10 – 10 = 30 – 10
6x = 20
6x/6 = 20/6
x = 10/3
(10/3, -2)
4. Find the x-and y-intercepts of the following equations.
2x + 3y = 12
Solution:
2x + 3y = 12
Put the value of x = 0
2 × 0 + 3y = 12
3y = 12
3y/3 = 12/3
y = 4
Therefore, y-intercept = (0, 4)
Now, put the value of y = 0
2x + 3 × 0 = 12
2x = 12
2x/2 = 12/2
x = 6
Therefore, x-intercept = (6, 0)
5. Find the x-and y-intercepts of the following equations. x + y = -2
Solution:
x + y = -2
Put the value of x = 0
0 + y = -2
y = -2
Therefore, y-intercept = (0, -2)
Put the value of y = 0
x + 0 = -2
x = -2
Therefore, x-intercept = (-2, 0)
6. Find the midpoint of each segment with the given endpoints.
(-10, 4) and (7, 1)
Solution:
(-10, 4) and (7, 1)
Midpoint = [(x_{1} + x_{2})/2, (y_{1} + y_{2})/2]= [(3 + 6)/2, (-6 + 3)/2]
= (9/2, -3/2)
Answer: (9/2, -3/2)
8. Decide whether the lines are parallel, perpendicular or neither.
x + 4y = 7 and 4x – y = 3
Solution:
x + 4y = 7
4y = -x + 7
y = (-1/4) x + 7
Slope of the equation x + 4y = 7 is -1/4.
Again, 4x – y = 3
y = 4x – 3
Slope of the equation 4x – y = 3 is 4.
Since multiplying both the slope of the equation = -1/4 × 4
= -1
Therefore, the given two equations are perpendicular to each other.
Answer: Perpendicular
9. The ship has coordinates (2,3) the equation of the other line is x+y=2 find the shortest distance from the ship to the line.
x + y = 2
x + y – 2 = 0
Distance from (2, 3) to the line x + y – 2 = 0
13. Simplify: 5 - 2 [8 - (2 x 2 - 4 x 4)]
Solution:
5 - 2 [8 - (2 x 2 - 4 x 4)]
= 5 - 2 [8 - (4 - 16)]
= 5 - 2 [8 - (-12)]
= 5 - 2 [8 + 12]
= 5 - 2 [20]
= 5 – 40
= -35
Answer: -35
14. Fill in the blank:
(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.
(b) To find the x-intercept of a line, we let....equal 0 and solve for
......; to find y-intercept, we let ......equal 0 and solve for.......
Solution:
(a) The point with coordinates (0,0) is called origin of a rectangular coordinate system.
(b) To find the x-intercept of a line, we let y equal 0 and solve for x ; to find y-intercept, we let x equal 0 and solve for y .
15. Name the quadrant, if any, in which each point is located.
(a) (1, 6)
(b) (-4, -2)
Solution:
(a) (1, 6) --------- I Quadrant.
(b) (-4, -2) --------- III Quadrant.
16. A restaurant meal for a group of people cost $85 total. This amount included a 6% tax and an 18% tip, both based on the price of the food. Which equation could be used to find f, the cost of the food?
A. 85 = 1.24f B. 85 = 0.24c C. 85 = 1.06f + 0.18 D. 85 = f + 0.24
17. Three friends share the cost of a pizza. The base price of the pizza is p and the extra toppings cost $4.50. If each person’s share was $7.15, which equation could be used to find p, the base price of the pizza?
A. 7.15 = 3p - 4.50
B. 7.15 = 1/3(p + 4.50)
C. 7.15 = 1/3p + 4.50
D. 7.15 = 3(p + 4.50)
Answer: B. 7.15 = 1/3(p + 4.50)
18. A tile setter is joining the angles of two tiles, A and B, to make a 90-degree angle. The degree measure of Angle A can be represented as 3y + 2 and of Angle B as 5y. Which equation represents this situation?
A. 90 = 3y +2 – 5y B. 3y + 2 = 90 + 5y C. 90 = 8y + 2 D. 5y + 2 = 90 + 3y
Answer: C. 90 = 8y + 2
19. One-fourth of the distance between two cities is 100 miles less than
two-thirds the distance between the cities. Which equation expresses
this situation?
1/4d - 100 = 2/3d ,
1/4d = 2/3d -100,
1/4d = 2/3d +100,
1/4d - 2/3d = 100
Answer: 1/4d = 2/3d -100
20. What value of b makes the equation that follows true?
x^{2} + bx – 35 = (x + 5)(x – 7)
A. -2 B. 12 C. 2 D. -12
Answer: A.
-2
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