Equations of a Line given Two PointsDate: 8/31/96 at 15:42:24 From: Anonymous Subject: Equations of Lines Please can you help my children? Many thanks in advance. Find the equation of the line through the two given points: (4,-1), (3,-6) The answer given in the textbook is: y = 5x-21 but we do not know two things: a) Is it right? b) How does one get to this answer? Zillions of thanks. Mal. from U.K Date: 9/1/96 at 4:6:50 From: Doctor Mike Subject: Re: Equations of Lines Greetings Mal., The answer to (a) is yes, the answer given is correct. For (b) you start by finding the slope of the line. This is a fraction where the numerator is the difference of the y-coordinates, and the denominator is the difference of the x-coordinates. Make sure you take the differences in the same order, like -1 -(-6) -1 + 6 5 ----------- = -------- = --- = 5. 4 - 3 4 - 3 1 The slope is usually written as m, so here m = 5. The form of the equation of a line you are asking about is called the slope-intercept form. This looks like y = mx + b where b is the y-intercept, which is the y-value where the line intersects the y-axis. That is, (0,b) is on the line. What we know so far is that the equation looks like y = 5x + b. So, what is b ? You can find that out by considering either of the points to be on the line. Let's try the first one (4,-1). Since the combination of x = 4 and y = -1 must be on the line with equation y = 5x+b, it must be true that -1 = 5(4)+b. That is, -1 equals 20+b. The only b satisfying that is b = -21. So the equation is y = 5x + (-21) , or simply y = 5x - 21. That's all there is to it. Pretty brill! I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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