
Re: Slope and Slope Intercept
Posted:
Jan 19, 1998 1:32 PM


Slope refers to lines and should have been a part of your algebra course. Slope is defined to be rise/run or, given two points on the line (x1,y1) and (x2,y2), the difference in y values divided by the difference in x values. Slope = (y2y1)/(x2x1) The main error students make is in not keeping the order of the points  it doesn't matter which comes first, y2 or y1, as long as numerator and denominator correspond. (y2y1)/(x2x1) = (y1y2)/(x1x2). The other common error is forgetting which difference is the numerator and which is the denominator. One of my students remembered it as "the twolegged man carries the onelegged man". Since slope is like climbing stairs, I remind students that they have to lift their leg first, then slide it forward.
The equation of a line, in standard form or slopeintercept form, is y = mx + b where m is the slope of the line and b is the yintercept, where the line crosses the vertical axis. Thus, the point (0,b) lies on the line. If you start with two points, you can calculate the slope. Now use the slope and one of the points and substitute into the slopeintercept form to find the value of b. For example, if the points were (x1,y1) and (x2,y2) as above, you can use either point to find b. y1 = m*x1 + b Once you find b, then you can write the equation of the line and find many other points on that line.
I am surprised that you never learned this in 8th grade or algebra. It is generally part of the curriculum.
Eileen Schoaff Buffalo State College

