Answer:
Explanation:
The student made two errors in graphing the equation y = -3x + 2:
1. Moving down instead of up: The y-intercept is the point where the line crosses the y-axis. In this case, the equation y = -3x + 2 clearly states that the y-intercept is 2. Therefore, the student should have started by plotting the point (0, 2) on the y-axis.
2. Moving left for a negative slope: The slope of the equation is -3, which means that for every 3 units you move down (negative y direction), you must also move 1 unit to the right (positive x direction). This creates a downward slant from left to right, not a horizontal move followed by a downward move.
To correct these errors:
fromfrom by plotting the y-intercept at (0, 2).
Since the slope is -3, for every 3 units you move down (y-axis), move 1 unit to the right (x-axis). For example, from (0, 2), move down 3 units (y-axis) to (-1, -1), then move 1 unit to the right (x-axis) to (-1, -1).
Repeat this process of moving down 3 units and then right 1 unit to plot more points on the line.
By following these steps, the student will correctly graph the equation y = -3x + 2.
Remember, the slope tells you the rise over run. In this case, for every 3 units down (negative rise), you must move 1 unit right (positive run), resulting in a downward slope from left to right.