Calculate the Slope of a Line – Practice Questions

The slope of a line is the direction and the steepness of the line. Slope is usually the letter m; 

Slope is calculated by finding the ratio of the “vertical change” to the “horizontal change” between two points on a line. Sometimes the ratio is expressed as a quotient (“rise over run”), giving the same number for every two points on the line. A line that is decreasing has a negative “rise” and a negative slope.

• If a line is horizontal the slope is zero.
• A line is decreasing if it goes down from left to right. The slope is negative, i.e. .
• A line is increasing if it goes up from left to right. The slope is positive, i.e. .
• If a line is vertical the slope is undefined

The rise of a line, between two points, is the difference between the height at those two points,  y₁ and y₂, so the equation is  (y₂ − y₁) = Δy. In basic geometry, we examine short distances, otherwise we would have to incorporate the curvature of the earth.  The run, is the difference in distance from a fixed point along a horizontal line, or (x₂ − x₁) = Δx.

The equation to calculate the slope of a line, m, is:

4. A
(x1, y1) = (-9, 6) & (x2, y2) = (18, -18)
Slope=(-18 – 6) / [18 – (-9)] = -24/27= -(8/9)