How to find the slope of a perpendicular line - Math

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Question

Any line that is perpendicular to must have a slope of what?

Answer

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. To find the slope, we must put the equation into slope-intercept form, , where equals the slope of the line. First, we must subtract from both sides of the equation, giving us . Next, we must divide both sides by , giving us . We can now see that the slope of this line is . Therefore, any line that is perpendicular to this one must have a slope of .

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Question

A line goes through the following and .

Find the slope of a line perpendicular to the line given.

Answer

The slope of a line perpendicular is the negative reciprocal of the given line.

Since the given slope is calculated as $\frac{8-5}{10-4}$=\frac{3}{6}$=\frac{1}{2}$ , then the slope of the perpendicular line would be .

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Question

What is the slope of any line perpendicular to $y=-$\frac{1}{2}$x+5$ ?

Answer

The slope of a perpendicular line is the negative reciprocal of the original slope.

The original slope is $-$\frac{1}{2}$$ .

The negative reciprocal of the original slope is:

$-$\frac{1}{-(\frac{1}${2})} = 2$

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Question

What is the slope of a line perpendicular to ?

Answer

The equation is a vertical line on the coordinate plane. Any line perpendicular to a vertical line is a horizontal line. Horizontal lines have slopes of zero.

The correct answer is .

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Question

Assume the points and form a line. A perpendicular line is drawn to intersect this line. What is the slope of the perpendicular line?

Answer

Write the slope formula and find the slope of the first line.

$m=\frac{y_2-y_1}{x_2-x_1}$=\frac{3-1}{2-1}$=\frac{2}{1}$=2$

The slope of the perpendicular line is the negative reciprocal of the original slope.

$-$\frac{1}{(2)}$ =-$\frac{1}{2}$$

Therefore, the slope of the perpendicular line is $-$\frac{1}{2}$$ .

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Question

A line passes through the points and . If a new line is drawn perpendicular to the original line, what will its slope be?

Answer

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

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Question

Find the slope of the line perpendicular to $y + $\frac{2}{3}$x = 12$ .

Answer

Put this equation into slope-intercept form, y = mx + b, to find the slope, m.

Do this by subtracting $$\frac{2}{3}$x$ from both sides of the equation:

$y = -$\frac{2}{3}$x + 12$

The slope of this line is $-$\frac{2}{3}$$ .

The slope of the perpendicular line is the negative reciprocal. Switch the numerator and denominator, and then multiply by :

$-$\frac{2}{3}$ \Rightarrow -$\frac{3}{2}$ \Rightarrow -$\frac{3}{2}$ \times -1 \Rightarrow $\frac{3}{2}$$

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Question

Which of the following is the equation of a line that is perpendicular to the line ?

Answer

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is (since it is in the form , where represents slope).

Then, we know that any line which is perpendicular to this will have a slope of $-$\frac{1}{3}$$ .

Thus, we can determine that $y = -$\frac{1}{3}$x + 10$ is the only choice with the correct slope.

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Question

Find the slope of this line:

Answer

Isolate for so that the equation now reads

$y=\frac{1}{4}$x-2$

The slope is $\frac{1}{4}$ .

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Question

Which of the following is perpendicular to the line described by

Answer

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be $-$\frac{1}{3}$$ .

The answer

$y=-$\frac{1}{3}$x+2$

is the only equation listed that has a slope of $-$\frac{1}{3}$$ .

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Question

Which of the following is perpendicular to the line described by

Answer

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be $\frac{1}{6}$ .

The answer

$y = $\frac{1}{6}$x+9$

is the only equation listed that has a slope of $\frac{1}{6}$ .

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Question

What will be the slope of the line perpendicular to $y=3x+\frac{1}{2}$$ ?

Answer

In standard form, the is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is . Therefore, the slope of the perpendicular line is $-$\frac{1}{3}$$ .

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Question

What is the slope of the line perpendicular to $y=\frac{2}{3}$x+\frac{1}{2}$$ ?

Answer

In standard form, is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is $\frac{2}{3}$ . Therefore, the slope of the perpendicular line is $-$\frac{3}{2}$$ .

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Question

Which of the following gives the slope of a line that is perpendicular to ?

Answer

Recall that the slopes of perpendicular lines are opposite reciprocals of one another. As a result, we are looking for the opposite reciprocal of . Thus, we can get that the opposite reciprocal is $\frac{1}{3}$ .

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Question

Any line that is perpendicular to must have a slope of what?

Answer

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. To find the slope, we must put the equation into slope-intercept form, , where equals the slope of the line. First, we must subtract from both sides of the equation, giving us . Next, we must divide both sides by , giving us . We can now see that the slope of this line is . Therefore, any line that is perpendicular to this one must have a slope of .

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Question

A line goes through the following and .

Find the slope of a line perpendicular to the line given.

Answer

The slope of a line perpendicular is the negative reciprocal of the given line.

Since the given slope is calculated as $\frac{8-5}{10-4}$=\frac{3}{6}$=\frac{1}{2}$ , then the slope of the perpendicular line would be .

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Question

What is the slope of any line perpendicular to $y=-$\frac{1}{2}$x+5$ ?

Answer

The slope of a perpendicular line is the negative reciprocal of the original slope.

The original slope is $-$\frac{1}{2}$$ .

The negative reciprocal of the original slope is:

$-$\frac{1}{-(\frac{1}${2})} = 2$

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Question

What is the slope of a line perpendicular to ?

Answer

The equation is a vertical line on the coordinate plane. Any line perpendicular to a vertical line is a horizontal line. Horizontal lines have slopes of zero.

The correct answer is .

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Question

Assume the points and form a line. A perpendicular line is drawn to intersect this line. What is the slope of the perpendicular line?

Answer

Write the slope formula and find the slope of the first line.

$m=\frac{y_2-y_1}{x_2-x_1}$=\frac{3-1}{2-1}$=\frac{2}{1}$=2$

The slope of the perpendicular line is the negative reciprocal of the original slope.

$-$\frac{1}{(2)}$ =-$\frac{1}{2}$$

Therefore, the slope of the perpendicular line is $-$\frac{1}{2}$$ .

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Question

A line passes through the points and . If a new line is drawn perpendicular to the original line, what will its slope be?

Answer

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

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