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In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i

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In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 14 Jun 2016, 17:01
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A
B
C
D
E

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In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-intercept of the line?

A. -9
B. -3
C. 0
D. 3
E. 9
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 14 Jun 2016, 22:02
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saiesta wrote:
In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-intercept of the line?

A. -9
B. -3
C. 0
D. 3
E. 9


x intercept 3 means the line passes through (3, 0). Slope of 3 means y co-ordinate increases by 3 units for every 1 unit rise in x co-ordinate or y co-ordinate decrease by 3 units for every 1 unit decrease in x co-ordinate.
At y intercept, x co-ordinate is 0. So if we reduce x by 3 (to go from 3 to 0), y will reduce by 9.

So, the line will pass through (0, -9)

Answer (A)
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 14 Jun 2016, 21:08
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Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 3.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*3 + b => b = -9. Hence A.
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 14 Jun 2016, 22:01
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y = mx+c
m=3 then y= 3x+c
put y=0 and x=3 get C as -9
this is the y intercept.
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 05 Aug 2017, 21:57
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x intercept 3 means the line passes through (3, 0).
Let the y be y and hence the line passes through (0, y).
Now slope=m=(y2-y1)/(x2-x1)
Hence 3=y/-3
So y=-9
A is the correct answer.
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 05 Aug 2017, 23:17
1
y=mx+c

substitute m=3 and point (3,0) in the above equation

0=3(3)+c

c=-9
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 06 Aug 2017, 02:04
Mathematical approach-
we know equation of a line is
y = mx + C
Now, as given at X =3, y = 0, we can get below,
0 = 3*3 + C => C = -9
Now, the question has asked for y intercept which is nothing but C in the equation y = mx+C.
we can even cross verify by substituting again -
y = 3*0 = (-9) = -9 Hence, A

One, intuitive approach is that- it is given slope =3
=> y/x = +3 meaning for every 1 unit change in X, there is a 3 unit change in y (in the same direction due to +ve sign)
Therefore, from x =3 (given intercept) to x =0 (when there is y intercept only), there is a decrease of 3 units of x. Hence y will decrease 3 time of it => 3 *3 = 9. Since the value is decreasing, y (will be negative) = -9.
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 28 Jan 2018, 15:18
Hi All,

You can deal with this prompt by either drawing a picture or by just creating an equation based on the facts that you know.

The slope-intercept formula for a line is Y = MX + B

From the prompt, we know that the slope is 3 and the X-INTERCEPT is 3 (meaning that X=3 when Y=0)

Y = MX + B
Y = 3X + B

0 = 3(3) + B
0 = 9 + B
-9 = B

So the Y-intercept is -9

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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 24 Mar 2019, 07:06
using point slope form....

y-y1=m(x-x1)

x intercept is (3,0)

y-0=3(x-3)

y=3x-9

-9 is the y intercept
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i  [#permalink]

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New post 10 Jul 2019, 17:51
We can apply some logic before touching formulas or anything.

See my attachment.

We are told that the slope is positive. We are also told that the x-intercept (where y=0) of the line is 3 i.e. x=3, y=0 (3,0). Therefore we can broadly plot this line enough to rule out a few answers:

We are asked for the y-intercept i.e. where x=0, what is the y-coordinate the line intercepts?

We can rule out (C), (D) and (E) based on our diagram.

Now solve for the y-intercept knowing it needs to be a negative value by plotting in the information we have
General form of line: y=mx +b
m (gradient) = 3
y=3x +b

we can determine b from the x-intercept
when x=3, y=0
0=3(3)+B
b=-9

y=3x -9
Y-intercept is where x=0
Y= 3(0) -9
Y= -9
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Re: In the xy-plane, a line has slope 3 and x-intercept 3. What is the y-i   [#permalink] 10 Jul 2019, 17:51
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