Finding the Equation of a Line
Date: 02/17/2005 at 21:24:00 From: Shelby Subject: How do I figure out Equation of a Line Word Problems? Find the equation of the line perpendicular to the graph of x - 3y = 6 and with an x intercept of 6. There are so many parts to it that I get steps mixed up! I have already had this problem explained to me and still don't get how you get the correct answer!
Date: 02/17/2005 at 22:32:23 From: Doctor Peterson Subject: Re: How do I figure out Equation of a Line Word Problems? Hi, Shelby. When you have a complex problem to solve, it helps to plan a strategy to get from what you know to what you need. Let's take inventory: what do we know? 1. We know the equation of a line. 2. We know the x-intercept of the line we're supposed to find. Now, where are we headed? We want to write the equation of a line perpendicular to the given line, with the given x-intercept. Next, we look at the goal, keeping in mind what supplies we are carrying with us, and ask what it would take to accomplish the goal: what do we WISH we had? Well, we know how to write the equation of a line if we know its slope and y-intercept. We don't have a y-intercept, but maybe we can get one. More important, the word "slope" reminds us of the word "perpendicular": part of our goal is to make a line perpendicular to the given one, and we know that the slope of a perpendicular line is the negative reciprocal of the other. So maybe it would be a good idea to find the slope of the line we were given. So let's make our first step to find the slope of that given line: 3. Find the slope of the given line, by writing it in slope-intercept form. 4. Take the negative reciprocal of that to get the slope of the desired line. That takes us a long way toward the goal; we'll have the slope and the x-intercept of the line we want. But it's unlikely you've learned the "slope-x-intercept" form of a line; I myself know it exists, but haven't memorized it. What other forms do we know? Perhaps you know the "point-slope" form of a line; if so, you can treat the x-intercept as a point and apply that form: 5. Use the x-intercept point (6,0) and the slope found in step 4 to write the equation of our line in point-slope form. 6. Rewrite that equation in whatever form is desired, such as slope-intercept. You may not have learned the point-slope form; if not, perhaps you have been taught an alternative way of finding a line through a point. One way is to write the slope-intercept form, treating "b" as an unknown; then you can take the known point and put its x and y into the equation, and solve the resulting equation for b. That gives you the y-intercept, and you have the equation. One way or another, you can solve the problem by taking one step at a time, gathering the information you need for the final assault on the goal. In general, to find an equation of a line, you'll need to know the slope and a point on the line. Find the slope of the given line, and then think about what you can use that for. Mapping out a strategy, rather than just blindly trying things, helps a lot in this process. I hope I've given you enough ideas to work out the rest for yourself. If you need more help, please write back and show me how far you got. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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