GRE Math : How to find the equation of a curve

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Example Questions

Example Question #2 : X And Y Intercept

What is the slope of the line whose equation is $\dpi{100} \small 8x+12y=20$ $\displaystyle \dpi{100} \small 8x+12y=20$?

Possible Answers:

$\dpi{100} \small -\frac{3}{2}$ $\displaystyle \dpi{100} \small -\frac{3}{2}$

$\dpi{100} \small \frac{2}{3}$ $\displaystyle \dpi{100} \small \frac{2}{3}$

$\dpi{100} \small \frac{3}{2}$ $\displaystyle \dpi{100} \small \frac{3}{2}$

$\dpi{100} \small -\frac{2}{3}$ $\displaystyle \dpi{100} \small -\frac{2}{3}$

$\dpi{100} \small 2$ $\displaystyle \dpi{100} \small 2$

Correct answer:

$\dpi{100} \small -\frac{2}{3}$ $\displaystyle \dpi{100} \small -\frac{2}{3}$

Explanation:

Solve for $\dpi{100} \small y$ $\displaystyle \dpi{100} \small y$ so that the equation resembles the $\dpi{100} \small y=mx+b$ $\displaystyle \dpi{100} \small y=mx+b$ form. This equation becomes $\dpi{100} \small -\frac{2}{3}x+\frac{5}{3}$ $\displaystyle \dpi{100} \small -\frac{2}{3}x+\frac{5}{3}$. In this form, the $\dpi{100} \small m$ $\displaystyle \dpi{100} \small m$ is the slope, which is $\dpi{100} \small -\frac{2}{3}$ $\displaystyle \dpi{100} \small -\frac{2}{3}$.

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Example Question #1 : X And Y Intercept

Which of the following equations has a $\displaystyle y$-intercept of $\displaystyle 13$?

Possible Answers:

$\displaystyle 3y=4x^2-16$

$\displaystyle 4x^2=12y+12$

$\displaystyle y=(x-4)^2-3$

$\displaystyle 2x^2-16y=5$

$\displaystyle 22x-2y=1$

Correct answer:

$\displaystyle y=(x-4)^2-3$

Explanation:

To find the $\displaystyle y$-intercept, you need to find the value of the equation where x=0 $\displaystyle x=0$. The easiest way to do this is to substitute in $\displaystyle 0$ for your value of $\displaystyle x$ and see where you get $\displaystyle 13$ for $\displaystyle y$. If you do this for each of your equations proposed as potential answers, you find that $\displaystyle y=(x-4)^2-3$ is the answer.

Substitute in $\displaystyle 0$ for $\displaystyle x$:

$\displaystyle y=(0-4)^2-3=(-4)^2-3=16-3=13$

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Example Question #111 : Coordinate Geometry

If $\displaystyle m$ is a line that has a $\displaystyle y$-intercept of $\displaystyle 3$ and an $\displaystyle x$-intercept of $\displaystyle 7$, which of the following is the equation of a line that is perpendicular to $\displaystyle m$?

Possible Answers:

$y=\frac{(7x+15)}{3}$ $\displaystyle y=\frac{(7x+15)}{3}$

$y=\frac{x+7}{3}$ $\displaystyle y=\frac{x+7}{3}$

$y=\frac{(3x+11)}{7}$ $\displaystyle y=\frac{(3x+11)}{7}$

$y=\frac{(-3x-24)}{7}$ $\displaystyle y=\frac{(-3x-24)}{7}$

$y=\frac{(7-7x)}{3}$ $\displaystyle y=\frac{(7-7x)}{3}$

Correct answer:

$y=\frac{(7x+15)}{3}$ $\displaystyle y=\frac{(7x+15)}{3}$

Explanation:

If $\displaystyle m$ has a $\displaystyle y$-intercept of $\displaystyle 3$, then it must pass through the point (0,3) $\displaystyle (0,3)$.

If its $\displaystyle x$-intercept is $\displaystyle 7$, then it must through the point (7,0) $\displaystyle (7,0)$.

The slope of this line is $\frac{0-3}{7-0}=-\frac{3}{7}$ $\displaystyle \frac{0-3}{7-0}=-\frac{3}{7}$.

Therefore, any line perpendicular to this line must have a slope equal to the negative reciprocal, which is $\frac{7}{3}$ $\displaystyle \frac{7}{3}$. Only $y=\frac{(7x+15)}{3}$ $\displaystyle y=\frac{(7x+15)}{3}$ has a slope of $\frac{7}{3}$ $\displaystyle \frac{7}{3}$.

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GRE Math : How to find the equation of a curve

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #2 : X And Y Intercept

Example Question #1 : X And Y Intercept

Example Question #111 : Coordinate Geometry

All GRE Math Resources

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