How do you know if two equations are parallel or perpendicular?

Two lines are parallel if and only if they have the same slope; this is not the case. They are perpendicular if and only if the product of their slopes is ; this is not the case, since . The lines are neither parallel nor perpendicular.

What are the perpendicular and parallel slope to?

The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals. This is a worked example of determining whether given lines are parallel or perpendicular.

Is a slope of 2 and perpendicular?

Correct answer: Explanation: Perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, the slope of the first line is -2. The reciprocal of -2 is -1/2, so the opposite of the reciprocal is therefore 1/2.

When two lines are parallel what is the solution?

When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.

How do you prove two lines are parallel?

If two lines are cut by a transversal and the alternate exterior angles are equal, then the two lines are parallel. Angles can be equal or congruent; you can replace the word “equal” in both theorems with “congruent” without affecting the theorem. So if ∠B and ∠L are equal (or congruent), the lines are parallel.

Do parallel lines have the same slope?

As mentioned above, parallel lines have the same slope. So, if we know the slope of the line parallel to our line, we have it made.

What is the perpendicular slope of?

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

How do you tell if a graph is perpendicular or parallel?

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

What is perpendicular to a slope of?

The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m.

What is the slope of 2 perpendicular lines?

Perpendicular lines are lines that intersect at right angles. The slope of the line with equation y=3x+2 is 3 . If you multiply the slopes of two perpendicular lines, you get −1 .

Why do parallel lines have no solution?

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution.

How do you calculate a perpendicular slope?

Find the slope of the given line. The perpendicular slope will be the opposite reciprocal of the original slope. Use the slope-intercept form (y = mx + b) and substitute in the given point and the new slope to find the intercept, b.

Do perpendicular lines have the same exact slope?

Perpendicular lines do not have the same slope . The slopes of perpendicular lines are different from one another in a specific way. The slope of one line is the negative reciprocal of the slope of the other line.

What is the formula for perpendicular slope?

The slope of a perpendicular line is the reciprocal of the slope of the original line. This simply means if the original slope is m, the reciprocal is 1/m. With this in mind, we can now manipulate the equation to determine the perpendicular line. y=mx+b -> y2= (1/m)x2+b

What makes a line parallel or perpendicular?

Lines cannot be always parallel. When two intersecting lines form four angles at their intersection points, all of which are equal and at right angles, then the lines are said to be perpendicular to each other. Two lines are perpendicular when they meet at right angles.