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In the ​ xy ​ -plane, what is the slope of the line whose

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In the ​ xy ​ -plane, what is the slope of the line whose [#permalink] New post 24 Jan 2017, 02:37
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In the xy-plane, what is the slope of the line whose equation is ​ \(3x - 2y = 8\) ?

A) \(-4\)

B) \(-\frac{8}{3}\)

C) \(\frac{2}{3}\)

D) \(\frac{3}{2}\)

E) \(2\)
[Reveal] Spoiler: OA

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Re: In the ​ xy ​ -plane, what is the slope of the line whose [#permalink] New post 26 Jan 2017, 18:37
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Explanation

You must know the equation of a line:

y = mx + b

Where: m is the slope, b is the y-intercept, and x and y are an x- and y-coordinate (x,y)

Convert the equation in the question to linear equation format:

\(3x - 2y = 8\)

\(-2y = -3x + 8\)

\(y = \frac{-3}{-2}x + \frac{8}{-2}\).

Since m = slope, the slope of this line is \(\frac{3}{2}\). Hence option D is correct.
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Re: In the ​ xy ​ -plane, what is the slope of the line whose [#permalink] New post 18 Feb 2019, 08:31
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Carcass wrote:


In the xy-plane, what is the slope of the line whose equation is ​ 3x - 2y = 8 ?

A) -4

B)\(-\frac{8}{3}\)

C) \(\frac{2}{3}\)

D) \(\frac{3}{2}\)

E) 2


I'd typically use Sandy's approach of rewriting the equation in slope y-intercept form.

That said, an alternate approach is to find two points ON the line and then find the slope between those two points.

GIVEN: 3x - 2y = 8
If x = 0, we get: 3(0) - 2y = 8
Solve for y to get y = -4
So, the point (0, -4) lies on the line.

Find a second point on the line.

GIVEN: 3x - 2y = 8
If x = 2, we get: 3(2) - 2y = 8
Solve for y to get y = -1
So, the point (2, -1) lies on the line.

Now use the slope formula to find the slope between (0, -4) and (2, -1)

Slope = [(-4) - (-1)]/(0 - 2)
= (-3)/(-2)
= 3/2

Answer: D

Cheers,
Brent
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Re: In the ​ xy ​ -plane, what is the slope of the line whose   [#permalink] 18 Feb 2019, 08:31
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