Sage-Tips

How do you tell if a line is parallel or perpendicular by the equation?

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.

How do you know if a line is perpendicular?

Perpendicular lines intersect at right angles to one another. To figure out if two equations are perpendicular, take a look at their slopes. The slopes of perpendicular lines are opposite reciprocals of each other.

What does it mean when 2 lines are perpendicular?

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Are two lines parallel if they are the same line?

If two lines are parallel to the same line, then they are parallel to each other.

What is the relationship between two lines that are perpendicular to the same line?

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. In a coordinate plane, two distinct nonvertical lines are parallel if and only if they have the same slope.

What is the value of P that makes two distinct lines parallel?

Or p = 10. Any value of p other than 10 will make the two distinct lines parallel. The two given lines : 3x – y = 5 and 6x -2y = p will be || to each other if the coefficients of x, y and constant terms are comparable. That is if : 3/6 = -1/-2 = 5/p ==> 5/p = 1/2 which gives p = 10 .

Are the lines y= -8x+5 and  are parallel or perpendicular?

Determine whether the lines y= −8x+ 5 and  are parallel, perpendicular, or neither. The given lines are written in y= mx+ bform, with m= −8 for the first line and m=  for the second line. Identify the slopes of the given lines. −8 ≠ , so the lines are not parallel. The opposite reciprocal of −8 is , so the lines are perpendicular.

How do you find two lines that are coincident?

Two lines will coincide if the equations representing them is exactly the same. => 3x – y – 5 = 0 & 2 (3x – y – p/2) = 0 will be coincident if p/2 = 5. Or p = 10. Any value of p other than 10 will make the two distinct lines parallel.

What are the solutions of linear equations in one variable?

Solution of Linear Equations in One Variable 1 Clear the fraction x – 5 = 3 (x – 1) 2 Simplify Both sides equations 2x – 5 = 3x – 3 x = 3x + 2 x – 3x = 2 3 Isolate x