Test: Slope Of A Line - Commerce MCQ

As A(3,y) and B(2,7) is parallel to C(-1,4) and D(0,6)
∴ Their slopes are equal
so, (y-7)/(3-1) = (4-6)/(-1-0)
y-7 = 2
y = 9

The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ.

Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope and lines with the same slope are parallel.

The equation of line which cuts intercepts of equal lengths on the axes is:

If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1.(since product of slopes of two perpendicular lines is -1) Therefore , m = 1.

Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of y-axis is m = tan 90° = ∞ i.e., not defined.

Slope = Change in y coordinates÷change in x coodinates
= (5-1)÷(2-x) =2
5-1 = 4-2x
0 = 2x
x=0

Slope of x-axis is m = tan 0° = 0.
 Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.

Let the slope of the line AB and AC are m₁ and m₂  respectively.

Then, 

Let θ be the angle between AB and BC. Then,

Slope of the points A and B is -2 and the lines are perpendicular then

m1×m2 = -1.

∴ the slope is 1/2