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 [tex]m=\frac{-A}{B}[/tex]
∵ The equation is 3x - 2y + 7 = 0
∴ A = 3 and B = -2
∴ The slope of the line is [tex]m=\frac{-3}{-2}[/tex]
∴ The slope of the line is [tex]m=\frac{3}{2}[/tex]
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 [tex]m=\frac{-2}{3}[/tex]
∵ [tex]\frac{3}{2}[/tex] × [tex]\frac{-2}{3}[/tex] = -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 [tex]m=\frac{-3}{2}[/tex]
∵ [tex]\frac{3}{2}[/tex] × [tex]\frac{-3}{2}[/tex] ≠ -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 [tex]m=\frac{-2}{-3}[/tex]
∴ [tex]m=\frac{2}{3}[/tex]
∵ [tex]\frac{3}{2}[/tex] × [tex]\frac{2}{3}[/tex] ≠ -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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