GMAT Math : Calculating whether point is on a line with an equation

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Example Questions

Example Question #67 :Coordinate Geometry

Solve forin the coordinate (3,y) on line 5x+2y=13 ?

Possible Answers:

Correct answer:

Explanation:

To solve forfor x=3 , we have to pluginto thevariable of the equation and solve for:

5(3)+2y=13

15+2y=13

2y=13-15

2y=-2

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Example Question #671 :Geometry

Solve forin the coordinate (x,1) on line 3y=4x+1 ?

Possible Answers:

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To solve forfor y=1 , we have to plug 1 into thevariable of the equation and solve for:

3y=4x+1

3(1)=4x+1

3=4x+1

3-1=4x

2=4x

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

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Example Question #672 :Geometry

Solve forin the coordinate (5,y) on line 14y-10x=20 ?

Possible Answers:

Correct answer:

Explanation:

To solve forfor x=5 , we have to pluginto thevariable of the equation and solve for:

14y-10x=20

14y-10(5)=20

14y-50=20

14y=20+50

14y=70

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Example Question #673 :Geometry

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?

Possible Answers:

Correct answer:

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:

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

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Example Question #674 :Geometry

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

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

Possible Answers:

Yes

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

Cannot be calculated from the provided information

Correct answer:

Yes

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!

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Example Question #675 :Geometry

Which of the following are points along g(x) if

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

Possible Answers:

(3,-28)

(-3,-28)

(3,28)

(2,4)

(4,64)

Correct answer:

(3,28)

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).

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GMAT Math : Calculating whether point is on a line with an equation

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #67 :Coordinate Geometry

Example Question #671 :Geometry

Example Question #672 :Geometry

Example Question #673 :Geometry

Example Question #674 :Geometry

Example Question #675 :Geometry

All GMAT Math Resources

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