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To find y in the graph

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To find y in the graph

by gmattesttaker2 » Wed Feb 19, 2014 6:56 pm
Hello,

For the following:

In the rectangular coordinate system above, if x = 4.8, then y =

(A) 3.0
(B) 3.2
(c) 3.4
(D) 3.6
(E) 3.8

OA: B


However, I thought it should be 3.8. Can you please help?

Thanks,
Sri
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by Patrick_GMATFix » Wed Feb 19, 2014 10:33 pm
If we have the equation of the line, we'll be able to find y given the value of x for any point on the line. Equation of the line is y = mx + b where m is the slope and b is the y-intercept. We already know that the y-intercept (where the line crosses the y-axis) is 0.

the two known points (0,0) and (3,2) allow us to find the slope: difference-in-y/difference-in-x = (2-0)/3-0) = 2/3. That's our m.

So the equation of this line is y = 2x/3. Now just plug-in the value of x to find y:

y = 2x/3
y = 2*4.8/3
y = 2*1.6
y = 3.2

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by GMATGuruNY » Thu Feb 20, 2014 4:43 am
gmattesttaker2 wrote:Hello,

For the following:

In the rectangular coordinate system above, if x = 4.8, then y =

(A) 3.0
(B) 3.2
(c) 3.4
(D) 3.6
(E) 3.8

OA: B
If a line passes through (0,0) and (x,y), EVERY point on the line must have coordinates in the following ratio:
y/x.

The line in the figure passes through (0,0) and (3,2).
Thus, every point on the line must have coordinates in the following ratio:
y/x = 2/3.
Implication:
For every point on the line, y = (2/3)x.

Result:
When x = 4.8, y = (2/3)(4.8) = 3.2.

The correct answer is B.
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by [email protected] » Thu Feb 20, 2014 4:14 pm
Hi Sri,

Both Mitch and Patrick have presented solutions that use ratios. The cool thing about "ratio math" is that it can be "set up" in lots of different ways. Here's another ratio to consider...

Since we're dealing with a straight line that intersects the Origin, any two points on that line will have the same ratio. The two points that we have are:

(3, 2)
(4.8, Y)

We can then write the ratio as:

3/4.8 = 2/Y

Now we can cross-multiply:

3Y = 9.6

Y = 3.2

Final Answer: B

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