Guidelines

What happens if two lines have the same slope?

What happens if two lines have the same slope?

Theorem 104: If two lines have the same slope, then the lines are nonvertical parallel lines. If two lines are perpendicular and neither one is vertical, then one of the lines has a positive slope, and the other has a negative slope. Also, the absolute values of their slopes are reciprocals.

Can two lines have the same slope and not be parallel?

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane). On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.

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How do you prove that two lines are the same line?

If two lines have a transversal which forms alternative interior angles that are congruent, then the two lines are parallel. If two lines have a transversal which forms corresponding angles that are congruent, then the two lines are parallel.

Does this mean that all lines with the same slope are the same line?

Because all lines with the same slope will slant at the same angle, parallel lines have the same slope. Perpendicular lines (lines that intersect at a 90 degree angle) have slopes that are negative reciprocals.

What happens if two lines have the same slope and y-intercept?

Same Line: If the two linear equations have the same slope (and the SAME y-intercept), the equations represent the same line. Since a line intersects with itself everywhere, there will be an infinite number of solutions (intersecting everywhere.)

What happens when two lines have the same slope and y-intercept?

If two equations have the same slope and the same y-intercept, then they are the same line, therefore meaning that they connect an infinite number of times on the graph. The equation is as follows: y=mx+b where “m” serves as the slope and “b” serves as the y-intercept.

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What is the relationship between two lines whose slopes are 3 and 1 3?

The slope of two perpendicular lines are negative reciprocals of each other. That means that you flip the fraction upside down and take the opposite of it. The reciprocal of 13 is 3 . The opposite of 3 is −3 .

What is the slope of the two lines are they equal or not?

If two distinct lines are parallel, the slopes of the lines are equal. Vertical lines will not be considered since their slopes are undefined and cannot be considered equal. If the lines are parallel horizontal lines, the slopes are both zero.

When two lines have slopes that are negative reciprocals?

If the slopes of two lines are negative reciprocals, the lines are perpendicular. since their slopes of 0 have undefined reciprocals. Vertical and horizontal lines are perpendicular.

How many solutions are there if the two lines have the same slope and y-intercept?

If the y-intercepts are the same, the two equations represent the same line and there are INFINITELY MANY SOLUTIONS.

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How do you know if two lines are parallel to each other?

Therefore, if the slopes of two lines on the Cartesian plane are equal, then the lines are parallel to each other. Thus, if two lines are parallel then, m1 m 1 = m2 m 2. Generalizing this for n lines, they are parallel only when the slopes of all the lines are equal.

What is the difference between parallel lines and perpendicular lines?

Parallel lines have the same slope while the slope of perpendicular lines are negative reciprocals and… Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane). Parallel Lines in greater depth.

Do parallel lines have the same slope and never intersect?

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).

How do you find the slope of a paralell line?

In the general equation of a line y = mx + b, the m represents your slope value. An example of paralell lines would therefore be: (1) y = mx + b (2) y = mx + c