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Re: Slope and Slope Intercept
Posted:
Jan 19, 1998 1:32 PM
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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 = (y2-y1)/(x2-x1) 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. (y2-y1)/(x2-x1) = (y1-y2)/(x1-x2).
The other common error is forgetting which difference is the numerator and
which is the denominator. One of my students remembered it as "the two-legged
man carries the one-legged 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 slope-intercept form, is y = mx + b
where m is the slope of the line and b is the y-intercept, 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 slope-intercept 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
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