This is probably the easiest concept to get across, once your students have become comfortable with converting linear equations into standard form. When we say "standard form," we have made sure that the A term has always been positive; however, it should be noted that as long as the equation is in the form of Ax + By = C, there will be no problems finding the slope regardless of the sign on either A or B.
Our students should be pros at finding the slope of a line while it is in slope-intercept form. For example, if we have y = 3x - 5, our students know immediately that the slope is 3.
As long as they are confident that the slope of this equation is 3, we should be able to manipulate the equation any way we want to and still have a slope of 3.
Well, let's go back and convert this equation to standard form. After subtracting 3x from both sides of the equation, we are left with -3x + y = -5. Just to stay consistent, we multiply both sides of the equation by -1 to arrive in the "standard form" we've been referring to. We now have, in standard form:
When we find slope in standard form, we take the A term, divide by B, then change the sign (or we just say -A/B.
In this example, we have -3/-1, which is the same as 3/1, or 3. From slope-intercept form, what did we expect to get? You guessed it: 3!!
Now we can find the slope of any of the equations we've worked on so far whether they are in standard form or not. We know how to convert to standard form, and we now know how to find the slope while in standard form.
Instead of my forcing another worksheet down your throat, go back and look at some of the examples on the previous worksheets and see if you can find the slope.
At this point, it would be easy to make an attack against this lesson because I have not mentioned a word about a y-intercept. But, if you go back and think about it, why do we really care what the y-intercept is anyway? The only thing that the y-intercept does for us is that it gives us a point to start with to plot an equation, mainly out of slope-intercept form. The y-intercept really is pretty much useless: it doesn't give us any zeroes; it doesn't say anything about the slope; it only gives us a point to look at when x = 0. And, we still may end up with FRACTIONS!!! This was the idea behind this lesson: to avoid those senseless fractions.