Today in class we talked about HW9.
For Part I problems, we were given the slope and a point on the line. Then we then had to find the equation for the line. Can you do this? If you need a refresher, visit this site. Here is a worksheet if you would like extra practice.
For Part II problems, we were given two points on a line. Then we then had to find the equation for the line. Can you do this? If you need a refresher, visit this site. Here is a worksheet if you would like extra practice.
In some of our classes today, the point-slope form of linear equations was brought up. If you would like to know more about point-slope form, visit this site.
We then examined strategies to determine if two lines were parallel. Are these equations parallel?
- 2x + 4y = 12
- 4x + 8y = 16
6 comments:
I was wondering how do we determine if two lines are parallel using the standard equation: Ax+By=C ?
The method is like changing the equation into slope-intercept form. In general form to slope-intercept (y=mx+b). The A and B values comprise the slope of "m". So, with variables Ax+By=C try to change this into slope-intercept form. So for example, the first step to get "y" on one side, would result in By=C-Ax. Isolate "y" in order to find the relationship. Understand? Still don't understand?
Anonymous 7:22pm, your response was one of the strategies that people discussed today in class -- change the equations from Standard form into slope-intercept form.
But can you find other ways to determine if two equations in standard form are parallel?
To Mr. Marti:
Perhaps I may clarify. The changing general form into slope intercept form is simply a way to conceptualize how to determine parallel lines for the student to figure out him/herself. Although this problem has many ways of approach, one goes as follows: Given, slope is the average rate of change in two points. Given, Ax+By=C. Therefore, if zero is substituted for x the y value point for zero is C/B. If zero is substituted for y the x value for zero is C/A. Thus, two points for general form that holds true is, (0,C/B) and (C/A,0). The change in y is (C/B)-0, or C/B. The change in x is 0-(C/A), or -C/A. Therefore, the slope is (C/B)/(-C/A), one can simplify this by dividing by the reciprocal. This gives us -A/B for slope. Therefore, if -A/B is the same value two equations containing A and B values in general form then the slope is equal. To determine parallel lines, the C value is the determining factor after slopes are equal. If two equations,both with equal values of Ax+By=C have the same slope as determined by -A/B, and the same C value, the equations are equal, as all terms will cancel out when both equations, thus meaning that for any x values for both equations, the same y value should exist for both equations. However, if the equations denotate that one is Ax+By=C and one is Ax+By=D, then Ax and By cancel, leaving D=C. In such a case, no x point will give the same y point for the other equation. This is denotated on a graph b y parallel lines. Perhaps this explaination is rather lenghthy but I do hope no mistakes were made.
anon 9:29,
Are you saying that if equations in standard form are parallel, then their values of A and B must be equal and their values for C must be different?
No.
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