How to find the equation of a curve

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GRE Quantitative Reasoning › How to find the equation of a curve

Questions 1 - 3

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

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

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

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

$\dpi{100} \small 2$

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

Explanation

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

Which of the following equations has a -intercept of ?

Explanation

To find the -intercept, you need to find the value of the equation where . The easiest way to do this is to substitute in for your value of and see where you get for . If you do this for each of your equations proposed as potential answers, you find that is the answer.

Substitute in for :

If is a line that has a -intercept of and an -intercept of , which of the following is the equation of a line that is perpendicular to ?

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

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

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

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

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

Explanation

If has a -intercept of , then it must pass through the point .

If its -intercept is , then it must through the point .

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

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

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