How to find the slope of parallel lines - GRE Quantitative Reasoning

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Question

What is the slope of a line parallel to the line: -15x + 5y = 30 ?

Answer

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

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Question

What is the slope of a line that is parallel to the line 11x + 4y - 2 = 9 – 4x ?

Answer

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

$\newline 11x+4y-2=9-4x \newline 4y=11-15x \newline y=\frac{11}{4}-\frac{15}{4}x \newline y=-\frac{15}{4}x+\frac{11}{4}$

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Question

In the standard (x, y) coordinate plane, what is the slope of a line parallel to the line with equation ?

Answer

Parallel lines will have equal slopes. To solve, we simply need to rearrange the given equation into slope-intercept form to find its slope.

$y=-\frac{9}{12}x-\frac{18}{12}$

$y=-\frac{3}{4}x-\frac{3}{2}$

The slope of the given line is $-\frac{3}{4}$ . Any lines that run parallel to the given line will also have a slope of $-\frac{3}{4}$ .

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Question

What is the slope of a line that is parallel to the line ?

Answer

Parallel lines have the same slope. The question requires you to find the slope of the given function. The best way to do this is to put the equation in slope-intercept form (y = mx + b) by solving for y.

First subtract 6x on both sides to get 3y = –6x + 12.

Then divide each term by 3 to get y = –2x + 4.

In the form y = mx + b, m represents the slope. So the coefficient of the x term is the slope, and –2 is the correct answer.

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Question

What is the slope of any line parallel to –6x + 5y = 12?

Answer

This problem requires an understanding of the makeup of an equation of a line. This problem gives an equation of a line in y = mx + b form, but we will need to algebraically manipulate the equation to determine its slope. Once we have determined the slope of the line given we can determine the slope of any line parallel to it, becasue parallel lines have identical slopes. By dividing both sides of the equation by 5, we are able to obtain an equation for this line that is in a more recognizable y = mx + b form. The equation of the line then becomes y = 6/5x + 12/5, we can see that the slope of this line is 6/5.

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Question

Quantity A: The slope of a line parallel to

Quantity B: The slope of a line perpendicular to

Which of the following is true?

Answer

For a question like this, it is easiest to start by putting each equation into the slope-intercept form. This is , where is the slope of the line.

Quantity A

Divide both sides by :

$y=-\frac{18}{4}x+\frac{13}{4}=-\frac{9}{2}x+\frac{13}{4}$

So, Quantity A is $-\frac{9}{2}$ . Parallel lines have equal slopes.

Quantity B

Divide both sides by :

$y=\frac{16}{6}x+\frac{15}{6}=\frac{8}{3}x+\frac{15}{6}$

Now, the perpendicular of a line has a slope that is opposite and reciprocal. Therefore, the slope for Quantity B is $-\frac{3}{8}$ . This is a smaller negative number than the value for Quantity A. Therefore, absolutely speaking, it is a larger value. Therefore, Quantity B is larger.

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Question

Quantity A: The slope of the line parallel to

Quantity B: The slope of the line parallel to $2y=-\frac{2}{3}x-14$

Which of the following is true?

Answer

To begin, put each equation into slope-intercept form, which is . The value for is the slope of the line. The lines that are parallel to each of our given lines will have equal slopes to their respective lines. (Parallel lines have equal slopes, after all.)

Quantity A

Divide both sides by :

$y=\frac{-5}{-15}x-\frac{12}{-15}=\frac{1}{3}x+\frac{12}{15}$

Therefore, the slope of the line parallel to this one is $\frac{1}{3}$ .

Quantity B

$2y=-\frac{2}{3}x-14$

Divide both sides by :

$y=-\frac{2}{6}x-7=-\frac{1}{3}x-7$

Therefore, the slope of the line parallel to this one is $-\frac{1}{3}$ . Therefore, Quantity A is larger.

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Question

A certain line has points at and . Which of the following lines is parallel to the so-called "certain" line?

Answer

To begin, we must first solve the for the slope of the original line. Use the formula for slope to do this:

$slope=\frac{rise}{run}=\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}$

Use the two points we were given:

$slope=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{1-(-5)}{(-6)-3}$

$=\frac{1+5}{-6-3}$

$=\frac{6}{-9}$

Reduce the fraction:

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

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

We are looking for any answer choice with a slope of $-\frac{2}{3}$ . The answer is $y=-\frac{2}{3}x + 6$ .

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Question

What is the slope of a line parallel to the line: -15x + 5y = 30 ?

Answer

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

Compare your answer with the correct one above

Question

What is the slope of a line that is parallel to the line 11x + 4y - 2 = 9 – 4x ?

Answer

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

$\newline 11x+4y-2=9-4x \newline 4y=11-15x \newline y=\frac{11}{4}-\frac{15}{4}x \newline y=-\frac{15}{4}x+\frac{11}{4}$

Compare your answer with the correct one above

Question

In the standard (x, y) coordinate plane, what is the slope of a line parallel to the line with equation ?

Answer

Parallel lines will have equal slopes. To solve, we simply need to rearrange the given equation into slope-intercept form to find its slope.

$y=-\frac{9}{12}x-\frac{18}{12}$

$y=-\frac{3}{4}x-\frac{3}{2}$

The slope of the given line is $-\frac{3}{4}$ . Any lines that run parallel to the given line will also have a slope of $-\frac{3}{4}$ .

Compare your answer with the correct one above

Question

What is the slope of a line that is parallel to the line ?

Answer

Parallel lines have the same slope. The question requires you to find the slope of the given function. The best way to do this is to put the equation in slope-intercept form (y = mx + b) by solving for y.

First subtract 6x on both sides to get 3y = –6x + 12.

Then divide each term by 3 to get y = –2x + 4.

In the form y = mx + b, m represents the slope. So the coefficient of the x term is the slope, and –2 is the correct answer.

Compare your answer with the correct one above

Question

What is the slope of any line parallel to –6x + 5y = 12?

Answer

This problem requires an understanding of the makeup of an equation of a line. This problem gives an equation of a line in y = mx + b form, but we will need to algebraically manipulate the equation to determine its slope. Once we have determined the slope of the line given we can determine the slope of any line parallel to it, becasue parallel lines have identical slopes. By dividing both sides of the equation by 5, we are able to obtain an equation for this line that is in a more recognizable y = mx + b form. The equation of the line then becomes y = 6/5x + 12/5, we can see that the slope of this line is 6/5.

Compare your answer with the correct one above

Question

Quantity A: The slope of a line parallel to

Quantity B: The slope of a line perpendicular to

Which of the following is true?

Answer

For a question like this, it is easiest to start by putting each equation into the slope-intercept form. This is , where is the slope of the line.

Quantity A

Divide both sides by :

$y=-\frac{18}{4}x+\frac{13}{4}=-\frac{9}{2}x+\frac{13}{4}$

So, Quantity A is $-\frac{9}{2}$ . Parallel lines have equal slopes.

Quantity B

Divide both sides by :

$y=\frac{16}{6}x+\frac{15}{6}=\frac{8}{3}x+\frac{15}{6}$

Now, the perpendicular of a line has a slope that is opposite and reciprocal. Therefore, the slope for Quantity B is $-\frac{3}{8}$ . This is a smaller negative number than the value for Quantity A. Therefore, absolutely speaking, it is a larger value. Therefore, Quantity B is larger.

Compare your answer with the correct one above

Question

Quantity A: The slope of the line parallel to

Quantity B: The slope of the line parallel to $2y=-\frac{2}{3}x-14$

Which of the following is true?

Answer

To begin, put each equation into slope-intercept form, which is . The value for is the slope of the line. The lines that are parallel to each of our given lines will have equal slopes to their respective lines. (Parallel lines have equal slopes, after all.)

Quantity A

Divide both sides by :

$y=\frac{-5}{-15}x-\frac{12}{-15}=\frac{1}{3}x+\frac{12}{15}$

Therefore, the slope of the line parallel to this one is $\frac{1}{3}$ .

Quantity B

$2y=-\frac{2}{3}x-14$

Divide both sides by :

$y=-\frac{2}{6}x-7=-\frac{1}{3}x-7$

Therefore, the slope of the line parallel to this one is $-\frac{1}{3}$ . Therefore, Quantity A is larger.

Compare your answer with the correct one above

Question

A certain line has points at and . Which of the following lines is parallel to the so-called "certain" line?

Answer

To begin, we must first solve the for the slope of the original line. Use the formula for slope to do this:

$slope=\frac{rise}{run}=\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}$

Use the two points we were given:

$slope=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{1-(-5)}{(-6)-3}$

$=\frac{1+5}{-6-3}$

$=\frac{6}{-9}$

Reduce the fraction:

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

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

We are looking for any answer choice with a slope of $-\frac{2}{3}$ . The answer is $y=-\frac{2}{3}x + 6$ .

Compare your answer with the correct one above

Question

What is the slope of a line parallel to the line: -15x + 5y = 30 ?

Answer

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

Compare your answer with the correct one above

Question

What is the slope of a line that is parallel to the line 11x + 4y - 2 = 9 – 4x ?

Answer

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

$\newline 11x+4y-2=9-4x \newline 4y=11-15x \newline y=\frac{11}{4}-\frac{15}{4}x \newline y=-\frac{15}{4}x+\frac{11}{4}$

Compare your answer with the correct one above

Question

In the standard (x, y) coordinate plane, what is the slope of a line parallel to the line with equation ?

Answer

Parallel lines will have equal slopes. To solve, we simply need to rearrange the given equation into slope-intercept form to find its slope.

$y=-\frac{9}{12}x-\frac{18}{12}$

$y=-\frac{3}{4}x-\frac{3}{2}$

The slope of the given line is $-\frac{3}{4}$ . Any lines that run parallel to the given line will also have a slope of $-\frac{3}{4}$ .

Compare your answer with the correct one above

Question

What is the slope of a line that is parallel to the line ?

Answer

Parallel lines have the same slope. The question requires you to find the slope of the given function. The best way to do this is to put the equation in slope-intercept form (y = mx + b) by solving for y.

First subtract 6x on both sides to get 3y = –6x + 12.

Then divide each term by 3 to get y = –2x + 4.

In the form y = mx + b, m represents the slope. So the coefficient of the x term is the slope, and –2 is the correct answer.

Compare your answer with the correct one above

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