Question
14. Determine if the lines are parallel, perpendicular or neither. y = -6x -8 and -x + 6y = 12
*
1 point
parallel
perpendicular
neither
*
1 point
parallel
perpendicular
neither
Answers
GPT 3.5
To determine if the lines are parallel, perpendicular, or neither, we need to compare the slopes of both lines.
The given line y = -6x - 8 is already in slope-intercept form (y = mx + b), where the slope (m) is -6.
To put the second line -x + 6y = 12 in slope-intercept form, we need to solve for y:
6y = x + 12
y = (1/6)x + 2
Comparing the slopes of the two lines, we have -6 vs 1/6.
Since the slopes are negative reciprocals of each other (opposite signs and reciprocal values), the lines are perpendicular to each other.
Therefore, the answer is: perpendicular.
The given line y = -6x - 8 is already in slope-intercept form (y = mx + b), where the slope (m) is -6.
To put the second line -x + 6y = 12 in slope-intercept form, we need to solve for y:
6y = x + 12
y = (1/6)x + 2
Comparing the slopes of the two lines, we have -6 vs 1/6.
Since the slopes are negative reciprocals of each other (opposite signs and reciprocal values), the lines are perpendicular to each other.
Therefore, the answer is: perpendicular.