What makes two lines parallel

First, let's find the slope of the line between and. The line between the points and :. This is the same slope, so the lines are parallel, and this is the correct answer.

We'll go through the rest of the answer choices for completeness. Here the slope is , so this is incorrect. This line is perpendicular, not parallel, to the line in question. The line between the points and : , also incorrect.

In order for two lines to intersect exactly once, they can't be parallel; thus, their slopes cannot be equal. If two lines have slopes that are indeed equal, these lines are parallel. Parallel lines either overlap infinitely or they never meet. If they overlap, they intersect at infinitely many points which is not the same as intersecting exactly once. In other words, we are looking for the system of equations with lines that are parallel, because then they will either intersect infinitely many times, or not at all.

If the lines are not parallel, they will intersect exactly once. To determine whether or not these lines are parallel, we need to find their slopes. Alternatively, you can solve for the slopes by rearranging both lines to slope-intercept form.

First let's subtract 6y from both sides. Thus, these two lines are parallel, so they will either intersect infinitely many times, or not at all. If we check all of the other systems of equations, we will find that each consists of lines that aren't parallel. Thus, all the other choices consist of lines that intersect exactly once. Line is given by the equation. In order for two lines to intersect, they cannot be parallel. To see whether or not two lines are parallel, we must compare their slopes.

Two lines are parallel if and only if their slopes are equal. Because the slope of this line is not equal to the slope of line q, the two lines aren't parallel. This line is in slope-intercept form. Thus, the slope of this line equals 4. Because the slope of this line is not the same as the slope of q, these lines will intersect somewhere. Thus, this line is parallel to q. However, just because two lines are parallel doesn't mean they will never intersect.

If two lines overlap, they are parallel, and they will intersect infinitely many times. This means that q passes through the point —1, —2. This means that this line overlaps with line q, and they intersect infinitely many times.

However, let's verify that these lines don't intersect. Let's see if this line passes through the point —1, —2. In other words, this line doesn't pass through the same point as q. 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. Horizontal and vertical lines are perpendicular to each other i. More classes on this subject Algebra 1 Formulating linear equations: Writing linear equations using the slope-intercept form Algebra 1 Formulating linear equations: Writing linear equations using the point-slope form and the standard form.

Search Math Playground All courses. All courses. Algebra 1 Discovering expressions, equations and functions Overview Expressions and variables Operations in the right order Composing expressions Composing equations and inequalities Representing functions as rules and graphs. Algebra 1 Exploring real numbers Overview Integers and rational numbers Calculating with real numbers The Distributive property Square roots. If you need more of a review on how to use this form, feel free to go to Tutorial Equations of Lines.

If your linear equation is written in this form, m represents the slope and b represents the y -intercept. Example 1 : Find the slope of any line that is a parallel and b perpendicular to the line.

Before we tackle finding the parallel and perpendicular slopes it really can help us out if we find the slope of the given line. Lining up the form with the equation we have been given, can you see what the slope is? Example 2 : Find the slope of the line that is a parallel and b perpendicular to the line. Lining up the form with the equation we got, can you see what the slope is?

Example 3 : Find the slope of the line that is a parallel and b perpendicular to the line. Do you remember what special type of line this equation is? It is a vertical line. If you need a review on vertical lines, feel free to go to Tutorial Graphing Lines.

Example 4 : Find the slope of the line that is a parallel and b perpendicular to the line. It is a horizontal line. If you need a review on horizontal lines, feel free to go to Tutorial Graphing Lines. We can use this form to plug into when we need to come up with a linear equation. What are the two things we need to write an equation of a line????

If you said any point on the line and the slope, you are correct. Now keep in mind that this is not the equation of our line but of a line parallel to our line. We needed to write it this way so we could get the slope.

And it looks like the slope is 4. Since our line is parallel to a line that has a slope of 4, our line also has a slope of 4. Make sure that you are careful when one of your values is negative and you have to subtract it as we did in line 2. Now keep in mind that this is not the equation of our line but of the line parallel to our line. These are practice problems to help bring you to the next level.

Passes through -7, 2 and is parallel to. The following are webpages that can assist you in the topics that were covered on this page:.