Calculating whether point is on a line with an equation

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

Questions 1 - 6

1

Which of the following are points along if

${}g(x)=4x^2-8$ .

Explanation

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)

${}g(x)=4x^2-8$

If we plug in 3 we get

${}g(x)=4(3)^2-8=4(9)-8=36-8=28$ ,

So our point is (3,28).

2

Solve for in the coordinate on line ?

Explanation

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

3

Solve for in the coordinate on line ?

$\frac{1}{2}$

Explanation

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

$x=\frac{1}{2}$

4

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

If the point $\left ( 16,y\right )$ is on $\overline{JK}$ , what is the value of y?

Explanation

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:

$m=\frac{y'-y}{x'-x}$

Plug in and calculate:

$\small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$

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

$\small 5=\frac{1}{2}*4+b$

$\small b=5-2=3$

So our answer is:

$\small y=\frac{x}{2}+3$

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

$\small \small y=\frac{16}{2}+3=8+3=11$

5

If is defined as follows, is the point $\left ( -2,5\right )$ on ?

$\small f(x)=4x+13$

Yes

No

f(x) is undefined at (-2,5)

Cannot be calculated from the provided information

Explanation

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

$\small f(x)=4x+13$

Becomes,

$\small \small 5=4*-2+13=-8+13=5$

So yes, it does!

6

Solve for in the coordinate on line ?

Explanation

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

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