Question

Which of the following lines are perpendicular to 3x-2y+7=0

Answer 1

The line 2x + 3y - 5 = 0 is perpendicular to the line 3x - 2y + 7 = 0

Step-by-step explanation:

If the two lines are perpendicular, then the product of their slopes is -1

1. The general form of the linear equation is Ax + By + C = 0, where

   A , B and C are integers

2. The slope of the line is $m=\frac{-A}{B}$

∵ The equation is 3x - 2y + 7 = 0

∴ A = 3 and B = -2

∴ The slope of the line is $m=\frac{-3}{-2}$

∴ The slope of the line is $m=\frac{3}{2}$

Let us find the slopes of the given equation to find which of them

perpendicular to the line above

∵ 2x + 3y - 5 = 0

∴ A = 2 , B = 3

∴ The slope of the line is $m=\frac{-2}{3}$

∵ $\frac{3}{2}$ × $\frac{-2}{3}$ = -1

∴ The line 2x + 3y - 5 = 0 is perpendicular to the line 3x - 2y + 7 = 0

∵ 3x + 2y - 8 = 0

∴ A = 3 , B = 2

∴ The slope of the line is $m=\frac{-3}{2}$

∵ $\frac{3}{2}$ × $\frac{-3}{2}$ ≠ -1

∴ The line 3x + 2y - 8 = 0 is not perpendicular to the line 3x - 2y + 7 = 0

∵ 2x - 3y + 6 = 0

∴ A = 2 and B = -3

∴ The slope of the line is $m=\frac{-2}{-3}$

∴ $m=\frac{2}{3}$

∵ $\frac{3}{2}$ × $\frac{2}{3}$ ≠ -1

∴ The line 2x - 3y + 6 = 0 is not perpendicular to the line 3x - 2y + 7 = 0

The line 2x + 3y - 5 = 0 is perpendicular to the line 3x - 2y + 7 = 0

Learn more:

You can learn more about slopes in brainly.com/question/12941985

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