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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]  24 Jan 2017, 02:37
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Question Stats:

75% (00:28) correct 25% (00:09) wrong based on 40 sessions

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]  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]  18 Feb 2019, 08:31
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Expert's post
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

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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