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SAT Math : SAT Mathematics

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Example Questions

Example Question #4 : How To Find The Equation Of A Perpendicular Line

Give the equation of a line perpendicular to $\dpi{100} \small y=2x-7$ .

Possible Answers:

$\dpi{100} \small y=-2x+7$

$\dpi{100} \small y=-2x-6$

None of the other answers

$\dpi{100} \small y=-\frac{1}{2}x$

$\dpi{100} \small y=2x+6$

Correct answer:

$\dpi{100} \small y=-\frac{1}{2}x$

Explanation:

The slope of a perpendicular line is the opposite reciprocal, therefore we are looking for a line with a slope of $\dpi{100} \small -\frac{1}{2}$ .

$\dpi{100} \small y=-\frac{1}{2}x$ is the only answer choice that satisfies this criteria.

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Example Question #5 : How To Find The Equation Of A Perpendicular Line

Find the equation of the line that is perpendicular to $\dpi{100} \small \frac{x}{2}+3=y$ and passes through (5, 6).

Possible Answers:

$\dpi{100} \small 2x-4=y$

$\dpi{100} \small \frac{1}{2}x+16=y$

$\dpi{100} \small -2x+16=y$

$\dpi{100} \small -2x-4=y$

$\dpi{100} \small -\frac{1}{2}x+16=y$

Correct answer:

$\dpi{100} \small -2x+16=y$

Explanation:

We know that the slope of the original line is $\dpi{100} \small \frac{1}{2}$

Thus the slope of the perpendicular line is the negative reciprocal of $\dpi{100} \small \frac{1}{2}$ , or –2.

Then we plug the slope and point (5, 6) into the form $\dpi{100} \small m\left ( x-x_{1} \right )=y-y_{1}$ , which yields $\dpi{100} \small -2\left ( x-5 \right )=y-6$

When we simplify this, we arrive at $\dpi{100} \small -2x+16=y$

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Example Question #1 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to $2x+5y=9$ through $(4,12)$ ?

Possible Answers:

$5x+2y=7$

$-3x-2y=5$

$-5x+2y=4$

$2x-5y=12$

$2x+5y=11$

Correct answer:

$-5x+2y=4$

Explanation:

We need to find the slope of the given equation by converting it to the slope intercept form: $y=-\frac{2}{5}x+\frac{9}{5}$ .

The slope is $-\frac{2}{5}$ and the perpendicular slope would be the opposite reciprocal, or $\frac{5}{2}$ .

The new equation is of the form $y=\frac{5}{2}x+b$ and we can use the point $(4,12)$ to calculate $b=2$ . The next step is to convert $y=\frac{5}{2}x+2$ into the standard form of $-5x+2y=4$ .

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Example Question #7 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to $y=-\frac{1}{3}x+2$ and passes through $(1,7)$ ?

Possible Answers:

$x+3y=2$

$x+y=7$

$2x-3y=-3$

$-3x-y=5$

$-3x+y=4$

Correct answer:

$-3x+y=4$

Explanation:

Perpendicular slopes are opposite reciprocals. The original slope is $-\frac{1}{3}$ so the new perdendicular slope is 3.

We plug the point $(1,7)$ and the slope $m=3$ into the point-slope form of the equation:

$y-y_{1}=m(x-x_{1})$

to get $y=3x+4$ or in standard form $-3x+y=4$ .

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Example Question #71 : Geometry

Solve the system of equations for the point of intersection.

x + y = 15

x - y = 3

Possible Answers:

(5,8)

(8,5)

(6,9)

(9,6)

(6,-1)

Correct answer:

(9,6)

Explanation:

First one needs to use one of the two equations to substitute one of the unknowns.

From the second equation we can derive that y = x – 3.

Then we substitute what we got into the first equation which gives us: x + x – 3 = 15.

Next we solve for x, so 2x = 18 and x = 9.

x – y = 3, so y = 6.

These two lines will intersect at the point (9,6).

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Example Question #431 : Sat Mathematics

Line A is perpendicular to $y=2x+1$ and passes the point $(0,1)$ . Find the -intercept of line A.

Possible Answers:

$1$

$1.5$

$0.5$

$2$

$2.5$

Correct answer:

$2$

Explanation:

We are given an equation of a line and told that line A is perpendicular to it. The slope of the given line is 2. Therefore, the slope of line A must be $-0.5$ , since perpendicular lines have slopes that are negative reciprocals of each other.

The equation for line A will therefore take the form y=-0.5x+b , where b is the y-intercept.

Since we are told that it crosses $(0,1)$ , we can plug in the point and solve for c:

1 = -0.5(0)+b

b=1

Then the equation becomes $y=-0.5x+1$ .

To find the x-intercept, plug in 0 for y and solve for x:

0=-0.5x+1

0.5x=1

$x=2$

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Example Question #432 : Sat Mathematics

What line is perpendicular to y = -2x + 5 through $\left ( 2,4 \right )$ ?

Possible Answers:

-x + 2y = 6

3x + y = 4

3x - 2y = 7

2x - y = 3

x - 2y = 5

Correct answer:

-x + 2y = 6

Explanation:

The slope of the given line is m = -2 , and the slope of the perpendicular line is its negative reciprocal, m = 1/2 . We take the new slope and the given point (2,4) and plug them into the slope-intercept form of a line, y = mx + b .

$4 = \frac{1}{2}\times 2+b$

b = 3

Thus, the perpendicular line has the equation $y = \frac{1}{2}x + 3$ , or in standard form, -x + 2y = 6 .

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Example Question #51 : Lines

In the xy-plane, the equation of the line n is –x+8y=17. If the line m is perpendicular to line n, what is a possible equation of line m?

Possible Answers:

y= -1/8x + 5

x= -8y + (17/8)

y= -8x + 5

y= 8x-17

Correct answer:

y= -8x + 5

Explanation:

We start by add x to the other side of the equation to get the y by itself, giving us 8y =17 + x. We then divide both sides by 8, giving us y= 17/8 + 1/8x. Since we are looking for the equation of a perpendicular line, we know the slope (the coefficient in front of x) will be the opposite reciprocal of the slope of our line, giving us y= -8x + 5 as the answer.

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Example Question #1 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to x + 3y = 6 and travels through point (1,5)?

Possible Answers:

y = 2/3x + 6

y = 2x + 1

y = 3x + 2

y = –1/3x – 4

y = 6x – 3

Correct answer:

y = 3x + 2

Explanation:

Convert the equation to slope intercept form to get y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: m_{1 *}m₂ = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

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Example Question #1 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to 3x + 5y = 15 and passes through (3,2) ?

Possible Answers:

$y = \frac{-3}{5}x + 2$

$y = \frac{5}{3}x - 3$

$y = \frac{1}{3}x - 5$

$y = \frac{3}{2}x - 2$

$y = \frac{2}{5}x + 4$

Correct answer:

$y = \frac{5}{3}x - 3$

Explanation:

Convert the given equation to slope-intercept form.

3x + 5y = 15

5y=-3x+15

$y=-\frac{3}{5}+3$

The slope of this line is $-\frac{3}{5}$ . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is $\frac{5}{3}$ .

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

$2 = \frac{5}{3}(3) + b$

2=5+b

b = -3

So the equation of the perpendicular line is $y = \frac{5}{3}x - 3$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #4 : How To Find The Equation Of A Perpendicular Line

Example Question #5 : How To Find The Equation Of A Perpendicular Line

Example Question #1 : How To Find The Equation Of A Perpendicular Line

Example Question #7 : How To Find The Equation Of A Perpendicular Line

Example Question #71 : Geometry

Example Question #431 : Sat Mathematics

Example Question #432 : Sat Mathematics

Example Question #51 : Lines

Example Question #1 : How To Find The Equation Of A Perpendicular Line

Example Question #1 : How To Find The Equation Of A Perpendicular Line

All SAT Math Resources

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