Calculating whether point is on a line with an equation - GMAT Quantitative Reasoning

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Question

Solve for in the coordinate on line ?

Answer

To solve for for , we have to plug into the variable of the equation and solve for :

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Question

Solve for in the coordinate on line ?

Answer

To solve for for , we have to plug 1 into the variable of the equation and solve for :

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Question

Solve for in the coordinate on line ?

Answer

To solve for for , we have to plug into the variable of the equation and solve for :

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Question

Consider segment which passes through the points and .

If the point is on , what is the value of y?

Answer

First, use the points to find the equation of JK:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:

Slope is found via:

Plug in and calculate:

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).

So our answer is:

To find y, we need to plug in 16 for x and solve:

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Question

If is defined as follows, is the point on ?

Answer

To find out if (-2,5) is on f(x), simply plug the point into f(x)

Becomes,

So yes, it does!

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Question

Which of the following are points along if

.

Answer

One way to solve this one is by plugging in each of the answer choices and eliminating any that don't work out. Begin with our original g(x)

If we plug in 3 we get

,

So our point is (3,28).

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