The student plotted the first point correctly at (-5, 8). However, the second point should have been plotted 4 units to the right and 3 units down from (-5, 8), not 3 units to the right and 4 units down. This would place the second point at (-1, 5). The line was then drawn correctly through these two points.
The student plotted the first point correctly at (-5, 8). However, the second point should have been plotted 4 units to the right and 3 units down from (-5, 8), which would be (-1, 5). Instead, the student plotted the second point 3 units to the right and 3 units down from (-5, 8), which is (-2, 5). This is a common mistake when graphing linear equations.
Here is a step-by-step explanation of how to graph the equation y + 5 = (x - 8) correctly:
Isolate y: Subtract 5 from both sides of the equation to get y = (x - 8) - 5.
Identify the slope and y-intercept: The equation is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is 1 and the y-intercept (b) is -5.
Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is -5, so the line crosses the y-axis at (0, -5).
Use the slope to rise and run: The slope tells you rise over run. In this case, the slope is 1, which means you rise 1 unit and run 1 unit to the right.
Plot the second point: Starting from the y-intercept, move up 1 unit and then right 1 unit to plot the second point. This point should be at (1, -4).
Connect the two points with a line: The line should pass through the y-intercept and the second point.