Slope

What is the formula to calculate the slope (m) between two points, (x1, y1) and (x2, y2), on a straight line?

• m = (y2 - y1) / (x2 - x1)
• m = (x2 - x1) / (y2 - y1)
• m = (x1 - y1) / (x2 - y2)
• m = (y1 - x1) / (y2 - x2)

Answer explanation

The slope formula is (y2 - y1) / (x2 - x1), which represents the change in y-coordinates divided by the change in x-coordinates between two points.

In a given figure, time and distance graph of a linear motion is given. Two positions of time and distance are recorded as, when T=0, D=3 and when T=2, D=8. Using the concept of slope, find the law of motion, i.e., how distance depends upon time.

• D = 2(T + 1)

• D = T + 3
• 2D = 5T + 6

• D = 2T + 6

Answer explanation

Since all three points are collinear, therefore their slopes are equal.

m1 = 8-3/3-0 = 5/2

m2 = D-3/T

According to above stated property, m1=m2

i.e. 5/2 = D-3/T

or 2D = 5T + 6

If two points on a straight line are (4, 7) and (-2, 1), what is the slope of the line?

• 1

• 3
• -1

• 1/2

Answer explanation

The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, it's (1 - 7) / (-2 - 4) = (-6) / (-6) = 1, so the slope is 1.

If a line is perfectly horizontal, what is the value of its slope?

Answer explanation

A horizontal line has no rise (change in y) because all points on the line have the same y-coordinate. Therefore, the slope is 0.

Two lines have slopes of 3/4 and -4/3, respectively. What can be said about their relationship?

• They are parallel
• They are perpendicular
• They have the same slope
• They have no relationship

Answer explanation

Two lines are perpendicular if the product of their slopes is -1. In this case, (3/4) * (-4/3) = -1, so the lines are perpendicular to each other.

Two lines have slopes m1 = √3 and m2 = 1/√3. What is the angle (θ) between these two lines?

• 120 degrees

• 30 degrees

• 60 degrees
• 150 degrees