Question

James graphed the line shown. Then he drew a second line through the point (6,-7) so that the lines formed a right angle. What are the equations of the lines James graphed?

a) y = 2x + 3 and y = 2x - 19
b) y = -3x + 3 and y = -1x - 4
c) y = 2x + 3 and y = -3x - 4
d) y = -4 and y = -x + 3

Answer 1

The equations of the lines James graphed are y = 2x + 3 and y = -3x - 4. To form a right angle with the given line, the slope of the second line should be the negative reciprocal of the slope of the given line. Using the point (6, -7) and the slope -1/2, we can find the equation of the second line.

Step-by-step explanation:

The equations of the lines James graphed are y = 2x + 3 and y = -3x - 4.

To form a right angle with the given line, the slope of the second line should be the negative reciprocal of the slope of the given line. The slope of the given line can be determined from the information provided, which is 2. The negative reciprocal of 2 is -1/2, so the slope of the second line is -1/2. Using the point (6, -7) and the slope -1/2, we can use the point-slope form of a linear equation to find the equation of the second line.

Finally, we simplify the equation to y = -3x - 4. Thus, the equations of the lines James graphed are y = 2x + 3 and y = -3x - 4. Therefore, the correct option is c) y = 2x + 3 and y = -3x - 4.