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A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?

A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)

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A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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GMATinsight wrote:
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?

A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)

Line passes through origin. Hence one point line passes through would be (0,0). Let $$(x1,y1) = (0,0)$$

Given Slope $$= \frac{1}{7}$$

Slope of line $$= \frac{y2 - y1}{x2 - x1}$$

$$\frac{1}{7} = \frac{y2 - 0}{x2 - 0}$$

$$\frac{y2}{x2} = \frac{1}{7}$$

Therefore point $$(x2,y2) = (7,1)$$

From the options, point that lies on line $$= (14,2)$$ . Answer (D) ...
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Re: A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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GMATinsight wrote:
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?

A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)

Let's write the equation of the line in slope y-intercept form y = mx + b, where m = the slope and b = the y-intercept.

So, m = 1/7
And, since the line passes through the origin (0,0), we know that b (the y-intercept) = 0
So, the equation of the line is: y = (1/7)x + 0
Or just y = (1/7)x

So, all points (x, y) ON the line will satisfy the equation y = (1/7)x
Let's check the answer choices.

A) (0, 7) plug x = 0 and y = 7 into the equation of the line to get: 7 = (1/7)(0) Doesn't work. So, (0,7) is NOT on the line.
B) (1, 7) plug x = 1 and y = 7 into the equation of the line to get: 7 = (1/7)(1) Doesn't work. So, (1,7) is NOT on the line.
C) (7, 7) plug x = 7 and y = 7 into the equation of the line to get: 7 = (1/7)(7) Doesn't work. So, (7,7) is NOT on the line.
D) (14, 2) plug x = 14 and y = 2 into the equation of the line to get: 2 = (1/7)(14) This WORKS. So, (2,14) IS on the line.

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Re: A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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Slope intercept form of the line y=mx+c
Line passes through origin thus we have c=0
y=mx
m=1/7
7y=x only D satisfies the equation.
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A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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GMATinsight wrote:
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?

A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)

Should you not remember the slope intercept formula (y = mx + b), or any other method, you do know two things:

1) The line passes through (0,0), so that is a point on the line; and

2) The slope is 1/7, rise/run, which means from any point on the line, such as (0,0), you can count one up and seven over to the right to find another point.

Do that twice, starting from (0,0). The first point you'll "land on" is (7,1). Then again count one up and seven over from that point, and you land on (14,2).

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Re: A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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An important formula.

If we know the slope of a line and one point (x1,y1) that it passes through, then the equation of the line is

y-y1=m(x-x1)

We know the line passes through origin (0,0).
Putting x1=0 and y1=0 we get the equation as

y=mx => y=(1/7)x

so for any point on the line, the y-coordinate will be 1/7 times the x-coordinate.

Checking the options, only D satisfies it (x-coordinate =14, y-coordinate=1/7 times 14 =2)

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Re: A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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Slope = m = 1/7

As the line passes through the origin, the y intercept is ZERO, which means b = 0

we know, y = mx+b

y = 1/7.x+0

or x/y = 7

Now, lets quickly check the options which satisfy this equation:

A) (0, 7) - Nope, x/y != 7
B) (1, 7) - Nope, x/y != 7
C) (7, 7) - Nope, x/y != 7
D) (14, 2) - Yes - x/y = 7
E) (7, 14) - Nope, x/y != 7

Hence, Answer is D
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Re: A line in the xy-plane passes through the origin and has a slope of 1/  [#permalink]

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_________________ Re: A line in the xy-plane passes through the origin and has a slope of 1/   [#permalink] 20 Oct 2018, 21:10
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