What is slope? How do you calculate?

What is slope? How do you calculate?

• A. The ratio of horizontal change to vertical change.
• B. The difference between y-values divided by the sum of x-values.
• C. The product of the vertical and horizontal changes.
• D. The quotient (Y2 - Y1) / (X2 - X1).

Answer: (D)

Slope is the rate at which y changes as x changes. It tells you how steep a line is and whether it rises or falls as you move to the right. You calculate it by comparing two points on the line and taking the vertical change divided by the horizontal change: slope = (y2 − y1)/(x2 − x1). For example, moving from (2, 3) to (5, 9) gives a vertical change of 6 and a horizontal change of 3, so the slope is 6/3 = 2, meaning y increases by 2 for every 1 unit you move to the right. If the line is vertical, the slope is undefined; if the line is horizontal, the slope is 0. Describing slope as the ratio of horizontal change to vertical change would be the reciprocal, which isn’t the standard slope. The sum or the product of changes isn’t how slope is defined.

Slope is the rate at which y changes as x changes. It tells you how steep a line is and whether it rises or falls as you move to the right. You calculate it by comparing two points on the line and taking the vertical change divided by the horizontal change: slope = (y2 − y1)/(x2 − x1). For example, moving from (2, 3) to (5, 9) gives a vertical change of 6 and a horizontal change of 3, so the slope is 6/3 = 2, meaning y increases by 2 for every 1 unit you move to the right. If the line is vertical, the slope is undefined; if the line is horizontal, the slope is 0. Describing slope as the ratio of horizontal change to vertical change would be the reciprocal, which isn’t the standard slope. The sum or the product of changes isn’t how slope is defined.