Question

two nonvertical lines have slopes m 1m 1 ​ and m 2m 2 ​ , respectively. the lines are parallel if and the are unequal; the lines are perpendicular if

Answer 1

Two non vertical lines have slopes m₁ and m₂ ​, respectively. The lines are parallel if "m₁ = m₂" and the "y-intercepts" are unequal; the lines are perpendicular if m₁ = 1/m₂.

What is slope of a line?

The slope of a line is a measurement of its steepness and direction.

The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.

Some key features regarding the slopes of the lines are-

1. Slope of Parallel Lines:

A set of parallel lines always has the same inclination angle. Assume we possess two parallel lines l1 and l2 in the reference plane, inclined at angles θ1  and θ2 with the x-axis, respectively, such that the, θ2 = θ1.

m1 = m2

Therefore, the slopes of the two given parallel lines are equal.

2. Slope of Perpendicular Lines:

A pair of perpendicular lines everytime form a 90 angle. Imagine we have two perpendicular lines l2 and l1 in the coordinate plane, inclined at angles θ1 and θ2 with the x-axis, respectively, so that the provided angles follow the external angle theorem, θ2 =  θ1 + 90.

m1 = tan θ1

m2 = tan (θ1 + 90º) = - cot θ1

m1 × m2 = -1

Therefore, the product of slopes of two given perpendicular lines is equal to -1.

To know more about the slopes, here

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