How do you know if two equations are 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 is the relationship of the equations of the same line?

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 is parallel line and perpendicular line?

Parallel lines are lines in a plane that are always the same distance apart. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

What happens when a line is perpendicular?

Perpendicular lines are lines that intersect at right angles. That is, the slopes of perpendicular lines are opposite reciprocals . (Exception: Horizontal and vertical lines are perpendicular, though you can’t multiply their slopes, since the slope of a vertical line is undefined.)

What happens when two equations are the same?

Systems of equations that have the same solution are called equivalent systems. Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

How do you determine if an equation is dependent or independent?

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

Is perpendicular and parallel the same?

Parallel lines are lines in a plane that are always the same distance apart. Perpendicular lines are lines that intersect at a right (90 degrees) angle. …

How do you write an equation for a line that is parallel?

Write an equation for a line that is parallel to and has a y-intercept of . The equation of a line can be written using the expression where is the slope and is the y-intercept. When lines are parallel to each other, it means that they have the same slope, so .

Can two lines have the same slope but different equations?

Their slopes are the same! The parallel line needs to have the same slope of 2. And that answer is OK, but let’s also put it in y = mx + b form: But this does not work for vertical lines I explain why at the end. Be careful! They may be the same line (but with a different equation), and so are not parallel.

How do you solve a parallel line with a slope of 2?

The parallel line needs to have the same slope of 2. We can solve it using the “point-slope” equation of a line: y − y1 = 2(x − x1) And then put in the point (5,4): y − 4 = 2(x − 5) And that answer is OK, but let’s also put it in y = mx + b form: y − 4 = 2x − 10.

Which equation has the same slope but different y-intercepts?

Parallel lines have the same slope but different y-intercepts. When the equations of two lines are the same they have infinitely many points in common, whereas parallel lines have no points in common. where is the slope. In this particular situation . Therefore we want to find an equation that has the same value and a different value.