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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) ---------

(b) (7, -5) ---------

**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 = [(xHere, x

= [(-10 + 7)/2, (4 + 1)/2]

= (-3/2, 5/2)

(3,-6) and (6, 3)

Solution:

(3,-6) and (6, 3)

Midpoint = [(x

Here, x

= [(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

= 3/√(1 + 1)

= 3/√2

= (3 × √2)/(√2 × √2)

= (3√2)/2 units.

Solution:

0.000000373

= 3.73 × 10

Solution:

5.347 x 10-8

= 5.347/100000000

= 0.00000005347

(3 x 10

Solution:

(3 x 10

= 9×10

= 3 × 3 × 10

**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

**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 .

(a) (1, 6)

(b) (-4, -2)

Solution:

(a) (1, 6) ---------

(b) (-4, -2) ---------

**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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