Find whether the lines $3 y - 4 x = 5$ $3y-4x=5$ and $4 y + 6 = 3 x$ $4y+6=3x$ are parallel or perpendicular?

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Find whether the lines $3 y - 4 x = 5$ $3y-4x=5$ and $4 y + 6 = 3 x$ $4y+6=3x$ are parallel or perpendicular?

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Answer 1 · 2016-04-07T04:09:13

Lines are neither parallel nor they are perpendicular to each other.

Explanation:

Converting $3 y - 4 x = 5$ $3y-4x=5$ to slope intercept form we get $y = \frac{4}{3} x + \frac{5}{3}$ $y=4/3x+5/3$ , hence its slope is $\frac{4}{3}$ $4/3$ .

Now converting $4 y + 6 = 3 x$ $4y+6=3x$ to slope intercept form we get $y = \frac{3}{4} x - \frac{6}{4}$ $y=3/4x-6/4$ , hence its slope is $\frac{3}{4}$ $3/4$ .

While slope of parallel lines is always equal, product of slopes of perpendicular lines is $- 1$ $-1$ . As neither slopes are equal nor their product is $- 1$ $-1$ , lines are neither parallel nor they are perpendicular to each other.

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Find whether the lines $3 y - 4 x = 5$ $3y-4x=5$ and $4 y + 6 = 3 x$ $4y+6=3x$ are parallel or perpendicular?

1 Answer

Explanation:

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Find whether the lines $3 y - 4 x = 5$ $3y-4x=5$ and $4 y + 6 = 3 x$ $4y+6=3x$ are parallel or perpendicular?