## The Slope of a Line
General Explanation
Look at the line below:
One property of a line is its "steepness." In algebra, steepness is defined by SLOPE. By definition, slope = change in y/change in x. The change in y and the change in x are shown in the graph below. Change in y = change in y coordinates = (-1-2) = -3 Change in x = change in x coordinates = (3-(-4)) = 7 So the slope of the line = -3/7 Sample Problem
The slope of the line connecting the points (a,-1) and (-2,-2) is 1/7. What is a?
Solution
First, write out the equation for slope:
slope = change in y/change in xNext, find the changes in y and x: Change in y: -2-(-1) = -2+1 = -1 Change in x: -2-aUse these values in the equation for slope: slope = -1/(-2-a) = 1/7Solve for a: -7 = -2 - a a = 5 |