Question
Which equation gives a line perpendicular to 5x + 2y = 8?
A. y = -5/2x + 3
B. y = 5/2x - 6
C. y = -2/5x + 1
D. y = 2/5x + 8
A. y = -5/2x + 3
B. y = 5/2x - 6
C. y = -2/5x + 1
D. y = 2/5x + 8
Answers
Answered by
GPT 3.5
The equation of a line perpendicular to 5x + 2y = 8 will have a slope that is equal to the negative reciprocal of the slope of the given line.
The given line can be rewritten in slope-intercept form as:
2y = -5x + 8
y = (-5/2)x + 4
The slope of this line is -5/2.
Therefore, the line perpendicular to this line will have a slope that is the negative reciprocal of -5/2, which is 2/5.
The equation y = 2/5x + 8 has a slope of 2/5, making it perpendicular to the given line.
Therefore, the correct equation that gives a line perpendicular to 5x + 2y = 8 is choice D.
The given line can be rewritten in slope-intercept form as:
2y = -5x + 8
y = (-5/2)x + 4
The slope of this line is -5/2.
Therefore, the line perpendicular to this line will have a slope that is the negative reciprocal of -5/2, which is 2/5.
The equation y = 2/5x + 8 has a slope of 2/5, making it perpendicular to the given line.
Therefore, the correct equation that gives a line perpendicular to 5x + 2y = 8 is choice D.