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The gradient of a line which is perpendicular to the line with…

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The gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

  • A. 3/2
  • B. -3/2
  • C. 2/3
  • D. -2/3

QUICK ANSWER…

C

SOLUTION 

The general form of the equation of a straight line is like this:

y = mx + c

Where m = gradient or slope,

And c = intercept on y-axis.

Now for a line that is perpendicular (that cuts through the line at exactly 90 degrees) to the straight line represented by y = mx + c, the slope will not be m, but -1/m

Now to solve this problem, let us reduce 3x + 2y + 1 = 0 to the form y = mx + c so that we can obtain m.

3x + 2y + 1 = 0

2y = -3x – 1

Dividing through by 2,

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The gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is correct.
  4. D is not the correct answer.

QUICK TIPS…

You may please note these/this:

  • If a line has a gradient of m, another line that is perpendicular to it will have a gradient of -1/m

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/ culled from 2018 JAMB-UTME mathematics question 32 /

The gradient of a line which is perpendicular to the line with... » QuizTablet
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