MATHEMATICS

JAMB 2008 - Question 32

Mathematics 2008 JAMB Past Questions - Question 32: Find the gradient of a line which is perpendicular to the line with the equation 3x+2y+1=0

Find the gradient of a line which is perpendicular to the line with the equation 3x+2y+1=0
A:
B:
C:
D:
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Correct Answer

D

Explanation

3x +2y +1=0y=mx +c2y = -3x-1y = 3/2 x - 1/2m=-3/2 Find the gradient of a line which is perpendicular to the line with the equation 3x+2y+1=0 To find the gradient of a line perpendicular to the line with the equation 3x + 2y + 1 = 0, we need to determine the slope of the given line and then find the negative reciprocal of that slope.First, let's rewrite the equation of the given line in slope-intercept form (y = mx + c), where m is the slope:3x + 2y + 1 = 02y = -3x - 1y = (-3/2)x - 1/2From the equation, we can see that the slope of the given line is -3/2.To find the slope of the line perpendicular to this line, we take the negative reciprocal of -3/2:Negative reciprocal = -1 / (-3/2)                  = 2/3Therefore, the gradient of the line perpendicular to the line with the equation 3x + 2y + 1 = 0 is 2/3.