What makes 2 lines parallel

Coincident lines are the same line. Two lines are perpendicular lines if they intersect at right angles. Given the functions below, identify the functions whose graphs are a pair of parallel lines and a pair of perpendicular lines.

Parallel lines have the same slope. Perpendicular lines have negative reciprocal slopes. Figure Skip to main content. Graphs of Linear Functions. Search for:. Given the equations of two lines, determine whether their graphs are parallel or perpendicular The two lines in Figure 18 are parallel lines : they will never intersect. Parallel lines. Perpendicular lines. Let's see what you can do with parallel and perpendicular. Note that two lines are parallel if their slopes are equal and they have different y -intercepts.

This form can be handy if you need to find the slope of a line given the equation. Slope of the parallel line: Since parallel lines have the same slope what do you think the slope of any parallel line to this line is going to be?

Pat yourself on the back if you said Slope of the perpendicular line: Since the slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of any perpendicular line to this line is?

Slope of the parallel line: Since parallel lines have the same slope what do you think the slope of the parallel line is going to be? Slope of the perpendicular line: Since the slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of the perpendicular line is? What is the slope of a vertical line?

If you said undefined, you are right on. Slope of the parallel line: Since parallel lines have the same slope, what do you think the slope of the parallel line is going to be? Pat yourself on the back if you said undefined. Slope of the perpendicular line: Since slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of the perpendicular line is? This one is a little trickier. Vertical lines and horizontal lines are perpendicular to each other.

The slope of the perpendicular line in this case would be the slope of a horizontal line which would be 0. The slope of the parallel line is undefined and the slope of the perpendicular line is 0. What is the slope of a horizontal line? If you said 0, you are right on. Pat yourself on the back if you said 0. The slope of the perpendicular line in this case would be the slope of a vertical line which would be undefined. The slope of the parallel line is 0 and the slope of the perpendicular line is undefined.

A line going through the point and having slope of m would have the equation. When writing an equation of a line, keep in mind that you ALWAYS need two pieces of information when you go to write an equation:. We have a point, however what about the slope? You are not going to get off that easily. Two parallel lines won't ever intersect. If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular.

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.