Graphing Linear Equations and Inequalities?

Question

((((heres the graph))))
http://i89.photobucket.com/albums/k202/lanez3/math.jpg

1: For Figure 1, which letter corresponds to the ordered pair (4, -3)?
I B H J


2: For Figure 1, what are the (x,y) coordinates of E?
(-1, -4) (1, 5) (-1, 4) (1, 4)


3: For Figure 1, in which Quadrant does point H lie?
none I II IV


4: For Figure 1, what are the coordinates of C?
(-5, -4) (-5, 4) (4, -5) (-4, -5)


5: What is the ordinate of Point I?
5 -5 2 -2


6: Which of the following ordered pairs is a solution of the equation: 2x - 3y = 12?
(0, 4) (8, 4/3) (-6, 0) (-3, -5)


7: Which best describes the graph of y = -10?
horizontal line
slanted line
vertical line
parabola


8: Which best describes the graph of x = 5?
horizontal line
slanted line
vertical line
parabola


9: Which of the following ordered pairs is on the line in Figure 2?
(-2, 2) (-1, 1) (3, -1) (1, 0)


10: What is the y-intercept of the line in Figure 2?
zero 1 2 3


11: What is the x-intercept of 2x - y = 1?
1 -1 zero 1/2


12: What is the y-intercept of x - 2y = -6?
2 3 -6 -3


13: Given the relation {(-2,10), (0,5), (1/2,1), (3,10)}, what is the domain?
{1, 5, 10}
{-2, 3, 0, 1}
{1/2, 5, 0, 3}
{-2, 0, 1/2, 3}


14: For the relation given in Question #13, what is the range?
{0, 5, 10}
{1, 5, 10}
{-2, 0, 1/2, 3}
{ -2, 5, 10}


15: In the relation given in Question #13, is it a function?
Yes No Sometimes Maybe


16: If f(x) = 2x - 11, what is f(5)?
zero
-1
1
2


17: Which describes the graph of y > x - 2?
the solid line y = x - 2 and the half-plane above it
the solid line y = x - 2 and the half-plane below it
the half-plane above the dashed line y = x - 2
the half-plane below the dashed line y = x - 2


18: Which describes the graph of 3x - 2y ≥ 6?
the solid line 3x - 2y = 6 and the half-plane above it
the solid line 3x - 2y = 6 and the half-plane below it
the half-plane above the dashed line 3x - 2y = 6
the half-plane below the dashed line 3x - 2y = 6


19: Which describes the graph of 2y ≤ x - 5?
the solid line 2y = x - 5 and the half-plane below it.
the solid line 2y = x - 5 and the half-plane above it.
the half-plane below the dashed line 2y = x - 5
the half-plane above the dashed line 2y = x - 5

Answer 1

1. J

2. (1, 4)

3. none. It lies on the x-axis.

4. (-4, -5)

5. 5

6. (8, 4/3)

7. Horizontal line

8. Vertical line

9. (-2, 2)

10. 1

11. -1

12. 3

13. {-2, 0, 1/2, 3}

14. {1, 5, 10}

15. Yes. In order for a relation to be a function, it must pass the vertical line test. That means that any one x value on our graph is related to only one y value. That does not mean that any one y value must be related to only one x value. That kind of relationship is known as a 1 to 1 function. which is a special case for a function. In this particular problem, the graph passes the vertical line test, so it is a function.

16. -1

17. the half-plane above the dashed line y = x - 2

18. the solid line 3x - 2y = 6 and the half-plane above it

19. the solid line 2y = x - 5 and the half-plane below it.

Answer 2

Think about how you've done inequalites on the number line. For instance, they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for linear inequalities are very much the same.