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

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Example Questions

Example Question #61 : Coordinate Geometry

Solve for $\displaystyle y$ in the coordinate (3,y) $\displaystyle (3,y)$ on line $\displaystyle 5x+2y=13$ ?

Possible Answers:

$\displaystyle -1$

$\displaystyle 1$

$\displaystyle -2$

$\displaystyle 2$

Correct answer:

$\displaystyle -1$

Explanation:

To solve for $\displaystyle y$ for x=3 $\displaystyle x=3$ , we have to plug $\displaystyle 3$ into the $\displaystyle x$ variable of the equation and solve for $\displaystyle y$ :

$\displaystyle 5(3)+2y=13$

$\displaystyle 15+2y=13$

$\displaystyle 2y=13-15$

2y=-2 $\displaystyle 2y=-2$

$\displaystyle y=-1$

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Example Question #61 : Lines

Solve for $\displaystyle x$ in the coordinate (x,1) $\displaystyle (x,1)$ on line 3y=4x+1 $\displaystyle 3y=4x+1$ ?

Possible Answers:

$\displaystyle -1$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 2$

$\displaystyle 1$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

To solve for $\displaystyle x$ for y=1 $\displaystyle y=1$ , we have to plug 1 into the $\displaystyle y$ variable of the equation and solve for $\displaystyle x$ :

3y=4x+1 $\displaystyle 3y=4x+1$

$\displaystyle 3(1)=4x+1$

3=4x+1 $\displaystyle 3=4x+1$

3-1=4x $\displaystyle 3-1=4x$

2=4x $\displaystyle 2=4x$

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

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Example Question #3 : Calculating Whether Point Is On A Line With An Equation

Solve for $\displaystyle y$ in the coordinate (5,y) $\displaystyle (5,y)$ on line $\displaystyle 14y-10x=20$ ?

Possible Answers:

$\displaystyle 70$

$\displaystyle 5$

$\displaystyle -5$

$\displaystyle -70$

Correct answer:

$\displaystyle 5$

Explanation:

To solve for $\displaystyle y$ for x=5 $\displaystyle x=5$ , we have to plug $\displaystyle 5$ into the $\displaystyle x$ variable of the equation and solve for $\displaystyle y$ :

$\displaystyle 14y-10x=20$

$\displaystyle 14y-10(5)=20$

$\displaystyle 14y-50=20$

$\displaystyle 14y=20+50$

14y=70 $\displaystyle 14y=70$

$\displaystyle y=5$

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Example Question #1 : Calculating Whether Point Is On A Line With An Equation

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

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

Possible Answers:

$\displaystyle -5$

$\displaystyle 5$

$\displaystyle 11$

$\displaystyle 0$

$\displaystyle -11$

Correct answer:

$\displaystyle 11$

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:

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

Plug in and calculate:

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

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

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

$\small b=5-2=3$ $\displaystyle \small b=5-2=3$

So our answer is:

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

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

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

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Example Question #4 : Calculating Whether Point Is On A Line With An Equation

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

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

Possible Answers:

Yes

Cannot be calculated from the provided information

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

Correct answer:

Yes

Explanation:

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

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

Becomes,

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

So yes, it does!

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Example Question #5 : Calculating Whether Point Is On A Line With An Equation

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

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

Possible Answers:

(3,28) $\displaystyle (3,28)$

$\displaystyle (-3,-28)$

(4,64) $\displaystyle (4,64)$

(3,-28) $\displaystyle (3,-28)$

(2,4) $\displaystyle (2,4)$

Correct answer:

(3,28) $\displaystyle (3,28)$

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)

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

If we plug in 3 we get

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

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 #61 : Coordinate Geometry

Example Question #61 : Lines

Example Question #3 : Calculating Whether Point Is On A Line With An Equation

Example Question #1 : Calculating Whether Point Is On A Line With An Equation

Example Question #4 : Calculating Whether Point Is On A Line With An Equation

Example Question #5 : Calculating Whether Point Is On A Line With An Equation

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