Parallel Lines - GRE Quantitative Reasoning

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.

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

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

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

The slope of the given line is . Any lines that run parallel to the given line will also have a slope of .

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.

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.

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 :

So, Quantity A is . Parallel lines have equal slopes.

Quantity B

Divide both sides by :

Now, the perpendicular of a line has a slope that is opposite and reciprocal. Therefore, the slope for Quantity B is . 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.

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 :

Therefore, the slope of the line parallel to this one is .

Quantity B

Divide both sides by :

Therefore, the slope of the line parallel to this one is . Therefore, Quantity A is larger.

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

Use the two points we were given:

Reduce the fraction:

We are looking for any answer choice with a slope of . The answer is .

First write the equation in slope intercept form. Add to both sides to get . Now divide both sides by to get . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is .

To be totally clear, solve both lines in slope-intercept form:

2x – 4y = 33; –4y = 33 – 2x; y = –33/4 + 0.5x

2x + 4y = 33; 4y = 33 – 2x; y = 33/4 – 0.5x

These lines are definitely not the same. Nor are they parallel—their slopes differ. Likewise, they cannot be perpendicular (which would require not only opposite slope signs but also reciprocal slopes); therefore, they are non-perpendicular intersecting.

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation ,

We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Because the given line has the slope of , the line parallel to it must also have the same slope.

There are several ways to solve this problem. You could solve all of the equations for . This would give you equations in the form . All of the lines with the same value would be parallel. Otherwise, you could figure out the ratio of to when both values are on the same side of the equation. This would suffice for determining the relationship between the two. We will take the first path, though, as this is most likely to be familiar to you.

Let's solve each for :

Here, you need to be a bit more manipulative with your equation. Multiply the numerator and denominator of the value by :

Therefore, , , and all have slopes of

Now, notice that the slope of the line that you have been given is . You know this because slope is merely:

However, for your points, there is no rise at all. You do not even need to compute the value. You know it will be . All lines with slope are of the form , where is the value that has for all points. Based on our data, this is , for is always —no matter what is the value for . So, the parallel answer choice is , as both have slopes of .

To begin, solve your equation for . This will put it into slope-intercept form, which will easily make the slope apparent. (Remember, slope-intercept form is , where is the slope.)

Divide both sides by and you get:

Therefore, the slope is . Now, you need to test your points to see which set of points has a slope of . Remember, for two points and , you find the slope by using the equation:

For our question, the pair and gives us a slope of :

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.

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

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

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

The slope of the given line is . Any lines that run parallel to the given line will also have a slope of .

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.

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.