Question

parts of the plane label the origin, quadrants, x-axis, and y-axis: graph ordered pair blank naming identify the ordered pair and quadrant of each point. graph with points a-f, table with columns point, ordered pair, quadrant discrete graph blank continuous graph blank

Explanation:

PART 1: Label the origin, quadrants, x - axis, and y - axis

• The origin is the point where the x - axis and y - axis intersect. In the given coordinate plane, the origin has coordinates \((0,0)\).
• The x - axis is the horizontal number line, and the y - axis is the vertical number line.
• The quadrants are the four regions formed by the intersection of the x - axis and y - axis. Quadrant I is where \(x>0\) and \(y > 0\), Quadrant II is where \(x<0\) and \(y>0\), Quadrant III is where \(x < 0\) and \(y<0\), and Quadrant IV is where \(x>0\) and \(y < 0\).

On the given graph:

• Mark the origin (the point where the two axes cross) as \((0,0)\).
• Label the horizontal line as the \(x\) - axis (with an arrow pointing to the right for positive direction and left for negative).
• Label the vertical line as the \(y\) - axis (with an arrow pointing up for positive direction and down for negative).
• Label the four regions as Quadrant I (top - right), Quadrant II (top - left), Quadrant III (bottom - left), and Quadrant IV (bottom - right).

PART 2: Identify the ordered pair and quadrant of each point

To find the ordered pair \((x,y)\) of a point, we:

• Find the \(x\) - coordinate by moving horizontally (left or right) from the origin. If we move right, \(x\) is positive; if we move left, \(x\) is negative.
• Find the \(y\) - coordinate by moving vertically (up or down) from the origin. If we move up, \(y\) is positive; if we move down, \(y\) is negative.

Point A:

Step 1: Find the x - coordinate

From the origin, move 3 units to the left (so \(x=- 3\))

Step 2: Find the y - coordinate

From the origin, move 4 units up (so \(y = 4\))
The ordered pair is \((-3,4)\). Since \(x<0\) and \(y>0\), it is in Quadrant II.

Point B:

Step 1: Find the x - coordinate

From the origin, move 2 units to the right (so \(x = 2\))

Step 2: Find the y - coordinate

From the origin, move 2 units down (so \(y=-2\))
The ordered pair is \((2, - 2)\). Since \(x>0\) and \(y<0\), it is in Quadrant IV.

Point C:

Step 1: Find the x - coordinate

From the origin, move 1 unit to the left (so \(x=-1\))

Step 2: Find the y - coordinate

From the origin, move 1 unit up (so \(y = 1\))
The ordered pair is \((-1,1)\). Since \(x<0\) and \(y>0\), it is in Quadrant II.

Point D:

Step 1: Find the x - coordinate

From the origin, move 5 units to the right (so \(x = 5\))

Step 2: Find the y - coordinate

From the origin, move 0 units up/down (so \(y = 0\))
The ordered pair is \((5,0)\). Points on the axes are not in any quadrant (it is on the x - axis).

Point E:

Step 1: Find the x - coordinate

From the origin, move 4 units to the left (so \(x=-4\))

Step 2: Find the y - coordinate

From the origin, move 3 units down (so \(y=-3\))
The ordered pair is \((-4,-3)\). Since \(x<0\) and \(y<0\), it is in Quadrant III.

Point F:

Step 1: Find the x - coordinate

From the origin, move 5 units to the left (so \(x=-5\))

Step 2: Find the y - coordinate

From the origin, move 0 units up/down (so \(y = 0\))
The ordered pair is \((-5,0)\). Points on the axes are not in any quadrant (it is on the x - axis).

Filling the table:

Point	Ordered Pair	Quadrant
B	\((2,-2)\)	IV
C	\((-1,1)\)	II
D	\((5,0)\)	None (on x - axis)
E	\((-4,-3)\)	III
F	\((-5,0)\)	None (on x - axis)

PART 3: Discrete and Continuous Graphs (General Explanation)

• Discrete Graph: A discrete graph consists of distinct, separate points. For example, if we are graphing…

Answer:

• The origin is the point where the x - axis and y - axis intersect. In the given coordinate plane, the origin has coordinates \((0,0)\).
• The x - axis is the horizontal number line, and the y - axis is the vertical number line.
• The quadrants are the four regions formed by the intersection of the x - axis and y - axis. Quadrant I is where \(x>0\) and \(y > 0\), Quadrant II is where \(x<0\) and \(y>0\), Quadrant III is where \(x < 0\) and \(y<0\), and Quadrant IV is where \(x>0\) and \(y < 0\).

On the given graph:

• Mark the origin (the point where the two axes cross) as \((0,0)\).
• Label the horizontal line as the \(x\) - axis (with an arrow pointing to the right for positive direction and left for negative).
• Label the vertical line as the \(y\) - axis (with an arrow pointing up for positive direction and down for negative).
• Label the four regions as Quadrant I (top - right), Quadrant II (top - left), Quadrant III (bottom - left), and Quadrant IV (bottom - right).

PART 2: Identify the ordered pair and quadrant of each point

To find the ordered pair \((x,y)\) of a point, we:

• Find the \(x\) - coordinate by moving horizontally (left or right) from the origin. If we move right, \(x\) is positive; if we move left, \(x\) is negative.
• Find the \(y\) - coordinate by moving vertically (up or down) from the origin. If we move up, \(y\) is positive; if we move down, \(y\) is negative.

Point A:

Step 1: Find the x - coordinate

From the origin, move 3 units to the left (so \(x=- 3\))

Step 2: Find the y - coordinate

From the origin, move 4 units up (so \(y = 4\))
The ordered pair is \((-3,4)\). Since \(x<0\) and \(y>0\), it is in Quadrant II.

Point B:

Step 1: Find the x - coordinate

From the origin, move 2 units to the right (so \(x = 2\))

Step 2: Find the y - coordinate

From the origin, move 2 units down (so \(y=-2\))
The ordered pair is \((2, - 2)\). Since \(x>0\) and \(y<0\), it is in Quadrant IV.

Point C:

Step 1: Find the x - coordinate

From the origin, move 1 unit to the left (so \(x=-1\))

Step 2: Find the y - coordinate

From the origin, move 1 unit up (so \(y = 1\))
The ordered pair is \((-1,1)\). Since \(x<0\) and \(y>0\), it is in Quadrant II.

Point D:

Step 1: Find the x - coordinate

From the origin, move 5 units to the right (so \(x = 5\))

Step 2: Find the y - coordinate

From the origin, move 0 units up/down (so \(y = 0\))
The ordered pair is \((5,0)\). Points on the axes are not in any quadrant (it is on the x - axis).

Point E:

Step 1: Find the x - coordinate

From the origin, move 4 units to the left (so \(x=-4\))

Step 2: Find the y - coordinate

From the origin, move 3 units down (so \(y=-3\))
The ordered pair is \((-4,-3)\). Since \(x<0\) and \(y<0\), it is in Quadrant III.

Point F:

Step 1: Find the x - coordinate

From the origin, move 5 units to the left (so \(x=-5\))

Step 2: Find the y - coordinate

From the origin, move 0 units up/down (so \(y = 0\))
The ordered pair is \((-5,0)\). Points on the axes are not in any quadrant (it is on the x - axis).

Filling the table:

Point	Ordered Pair	Quadrant
B	\((2,-2)\)	IV
C	\((-1,1)\)	II
D	\((5,0)\)	None (on x - axis)
E	\((-4,-3)\)	III
F	\((-5,0)\)	None (on x - axis)

PART 3: Discrete and Continuous Graphs (General Explanation)

• Discrete Graph: A discrete graph consists of distinct, separate points. For example, if we are graphing the number of students in a class (which can only be whole numbers), the graph will have points that are not connected. The domain and range of a discrete graph are usually sets of individual values (like integers).
• Continuous Graph: A continuous graph is a graph where the points are connected, forming a line or a curve. For example, if we are graphing the distance traveled by a car over time (where time and distance can take on any real - number value in a certain interval), the graph will be a continuous line. The domain and range of a continuous graph are usually intervals of real numbers.

If we were to graph a discrete relationship (e.g., number of books sold per day), we would plot individual points for each day and the number of books sold on that day. If we were to graph a continuous relationship (e.g., temperature over time), we would draw a connected line or curve to show how temperature changes smoothly over time.