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Magazine Chapter 3: Problem 30
Graph each ordered pair on the same coordinate system. Label the axes; write a scale for each axis. \((4,-3)\)
Short Answer
Expert verified
Plot the point \( (4, -3) \) by moving 4 units right and 3 units down from the origin, and label axes.
Step by step solution
01
Identify the Ordered Pair
The given ordered pair is \( (4, -3) \). It consists of an x-coordinate (4) and a y-coordinate (-3).
02
Draw the Coordinate Axes
Draw two perpendicular lines intersecting at the origin (0,0). Label the horizontal line as the x-axis and the vertical line as the y-axis.
03
Label the Scale
Choose a suitable scale for the axes, for example, each unit on both axes can be represented by one grid square. Label the units on both axes adequately.
04
Locate the x-coordinate
Starting from the origin, move 4 units to the right along the x-axis since the x-coordinate is positive.
05
Locate the y-coordinate
From the point \( x = 4 \), move 3 units down along the y-axis since the y-coordinate is negative.
06
Plot the Point
Mark the point where the horizontal line from \( x = 4 \) intersects with the vertical line from \( y = -3 \). This is the point \( (4, -3) \). Add a label to this point.
07
Verify the Point
Ensure the point is correctly plotted by checking that it is located 4 units to the right of the origin and 3 units down.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Coordinate Plane
The coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. This plane is defined by two perpendicular number lines that intersect at a point called the origin. These number lines are called axes. The horizontal axis is the x-axis and the vertical axis is the y-axis. By using these axes, we can locate any point in this plane using ordered pairs. These pairs are written as \( (x, y) \), where \( x \) is the x-coordinate (horizontal position) and \( y \) is the y-coordinate (vertical position). Imagine this plane as a map: by following the coordinates, you can find the exact location of each point.
X-axis and Y-axis
The x-axis and y-axis divide the coordinate plane into four quadrants. Each axis serves as a reference line to locate points. The x-axis is the horizontal line that runs left (negative) and right (positive) from the origin. The y-axis is the vertical line that runs up (positive) and down (negative) from the origin.
- The origin, labeled \( (0, 0) \), is where the x-axis and y-axis intersect.
- Positive x-values are to the right of the origin.
- Negative x-values are to the left of the origin.
- Positive y-values are above the origin.
- Negative y-values are below the origin.
Plotting Points
Plotting points on the coordinate plane is like playing a game of connect-the-dots. Each point is defined by an ordered pair \( (x, y) \). To plot a point:
- Start at the origin (0,0).
- Move along the x-axis to the x-coordinate.
- From this position on the x-axis, move vertically to the y-coordinate.
- Mark this position as a point.
Scaling Axes
Scaling the axes means choosing the units to represent distances on the coordinate plane. A scale ensures consistency in spacing between points:
- Decide on a suitable scale for both the x-axis and y-axis. Commonly, each grid square could represent 1 unit.
- Label the numbers on both axes so each point is clear and precise.
- Keep the scales for both axes the same to maintain the accuracy of plotted points.
Labeled Coordinates
Labeled coordinates help in easily identifying points on the plot. Once a point is plotted, it's typically labeled with its coordinates for clarity. This practice helps in cross-checking the accuracy of the plot.
- Plot the point by following the x and y movements.
- After plotting, write the coordinates next to the point, such as \( (4, -3) \).
- This helps anyone reading the graph to quickly understand the location of the points.
