Describe and correct the error a student made when graphing the linear equation y=-3/1x-6
steps the student took:
plot the y intercept at (0,6)
plot a second point 3 units down and 4 units right from (0,6) at (4,3)
connect the points with the line
The error the student made is in the steps taken to plot the second point. They correctly plotted the y-intercept at (0,6), but mistakenly plotted the second point 3 units down and 4 units right from (0,6) at (4,3).
To correct the error, we need to make sure we are using the correct slope. The slope of the linear equation y = -3x - 6 is -3. This means that for every 1 unit we move to the right, we need to move 3 units down.
Given that the y-intercept is (0,6), we can use this information to find the second point. By moving 1 unit to the right from (0,6), we get (1,3) since we move 3 units down according to the slope. By connecting the y-intercept (0,6) and the correct second point (1,3), we can correctly graph the line.