Complete the table and then graph the function. y = 3x X Y 1 2 3 Click to select points on the graph. y 10 9 8 7
The Correct Answer and Explanation is:
Completed Table and Graph:
| x | y |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
Explanation
Completing the Table
The first step is to complete the table of values using the given function, y = 3x. This equation describes a relationship where the value of y is always three times the value of x. To find the corresponding y-value for each x-value in the table, one must substitute the x-value into the equation and solve for y.
- For x = 1: Substitute 1 for x in the equation: y = 3 * 1. The result is y = 3. This gives the coordinate pair (1, 3).
- For x = 2: Substitute 2 for x in the equation: y = 3 * 2. The result is y = 6. This gives the coordinate pair (2, 6).
- For x = 3: Substitute 3 for x in the equation: y = 3 * 3. The result is y = 9. This gives the coordinate pair (3, 9).
These calculations provide the points needed to plot the function on the graph.
Graphing the Function
The second step is to plot the coordinate pairs from the completed table onto the graph and draw the function’s line. Each pair (x, y) represents a single point on the coordinate plane. The x-value determines the horizontal position (left or right), and the y-value determines the vertical position (up or down).
- Plot the point (1, 3): Start at the origin (0,0), move 1 unit to the right along the x-axis, and then move 3 units up parallel to the y-axis. Mark this location with a point.
- Plot the point (2, 6): From the origin, move 2 units to the right along the x-axis, and then move 6 units up. Mark this location.
- Plot the point (3, 9): From the origin, move 3 units to the right along the x-axis, and then move 9 units up. Mark this final location.
Since the equation y = 3x is a linear function, its graph is a straight line. After plotting the three points, a straight line can be drawn passing through all of them. This line is the visual representation of the function y = 3x.
