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Graphing Linear Equations

Please see the attached file for the fully formatted problems.
1. a) Determine if the ordered pair (2, ¼) is a solution of the equation
(1/8)x + 3y = 1
b) Explain why or why not the pair is a solution.
2. a)Graph or describe fully the graph of the equation y = (2/3)x + 1.
b) Show the table method with values for x of 0, -3, and -6 to plot points.

3. For the graph shown, identify the:
a) x - intercept
b) y - intercept

4.
For the graph shown, identify the:
a) x - intercept b) y - intercept

5. For the equation 6x - 4y = 12, identify
a) x - intercept

b) y - intercept

6.
Choose the best graph of the equation -2x - y = 3.

a) b)

c) d)

7. Choose the best graph of the equation of x = -1.

a) b)

c) d)

8. Choose the best graph of the equation of y = 2.

a) b)

c) d)

9. Using the slope formula, find the slope of the line passing through the points (-2,-4) and (3, -1).

10 Using the slope formula, find the slope of the line passing through the points (3, 4) and (3, 1).

11 For the equation 5x - 4y = 8, find the
a) slope
b) y-intercept
12 a) Are the lines 2x - 4y = 6 and 4x - 8y = 6 parallel?

b) Why or why not?

13 a) Determine the slopes of each pair of points.
(0, -1) and (1, 2)

(2, -1) and (1, 1)

b)Are the lines through each pair of points are parallel?
Justify your answer.

14 For the line passing through the points (2, 0) and (5,3), write the equation of the line in:
a) point-slope form

b) slope-intercept form
15 A plain cheese pizza costs $8.00. Each additional topping costs $0.75.
a) Write the equation of the line that models the cost, y, in dollars, of a pizza with x toppings.

b) For your equation in a), what does the ordered pair (2, 9.50) represent?

16 Choose the best graph of the inequality -4x + y < -4.

a) b)

c) d)

17
Choose the best graph of the inequality y > -2x.

a) b)

c) d)

18 Choose the best graph of the inequality x < 3.

a) b)

c) d)

19 Write a paragraph explaining how to use the slope and y-intercept to write an equation.
Be accurate so that one could write the equation from your description/instructions.

20
Write a paragraph explaining how to use the slope and y-intercept to draw a graph.
Be accurate so that one could draw the graph from your description/instructions.

The following graph shows the balance in a bank account (y), in dollars, x days after the account was opened.

21 From the graph above,
a) What does the x-intercept represent?
b) What does the y-intercept represent?

22 From the graph above:
a) Where is the minimum?

b) What does it represent?

23 Create a real world situation which would describe the inequality graph below.

24 Discuss the meaning of x-axis, y-axis, y-intercept and the shaded area as it relates to your situation described in #23.

Graph for Problems 23 - 24

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1. a) Determine if the ordered pair (2, ¼) is a solution of the equation
(1/8)x + 3y = 1
b) Explain why or why not the pair is a solution.

Solution:
Yes, it is a solution.

Put x = 2, y = ¼ in left hand side of equation
(1/8)x + 3y = (1/8)*2 + 3*(1/4) = ¼ + ¾ = 1

Thus, it is a solution.

2. a)Graph or describe fully the graph of the equation y = (2/3)x + 1.
b) Show the table method with values for x of 0, -3, and -6 to plot points.

Solution:
Table of values is
x y
0 (2/3)*0 + 1 = 1
-3 (2/3)*(-3) + 1 = -2 + 1 = -1
-6 (2/3)*(-6) + 1 = -4 + 1 = -3

The graph is shown below:

3.
For the graph shown, identify the:
a) x - intercept
b) y - intercept

Solution:

x-intercept: (4, 0)
y-intercept: (0, -5)

4.
For the graph shown, identify the:
a) x - intercept b) y - intercept

(a) x-intercept: none
(b) y-intercept: (0, -2)
5. For the equation 6x - 4y = 12, identify
a) x - intercept
Put y = 0
6x = 12
X = 2
x-intercept = (2, 0)

b) y - intercept
Put x = 0
-4y = 12
y = -3
y-intercept = (0, -3)

6.
Choose the best graph of the equation -2x - y = 3.

a) b)

c) d)

Answer: (d)

7. Choose the best graph of the equation of x = -1.

a) b)

c) ...

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