Determining SlopeDate: 05/19/99 at 01:47:17 From: Teresa Jaramillo Subject: Determining the slope (3,4) (4,6) (18,-4) (6,-10) (14,3) (-11,3) (3/4,1) 3/4,-1) Finding r (9,r) (6,3) m = -1/3 (r,7) 11,r) m = -1/5 I don't understand how to do this. Please help me. Date: 05/19/99 at 15:37:46 From: Doctor Rick Subject: Re: Determining the slope Hi, Teresa. You're completely lost. Let's try to help you find your way. I'll draw you a map, I mean, graph. Here is the first problem: y | 6 + X (4,6) | /| 5 + / |2 | / | 4 + (3,4) X---+ | : 1 : 3 + : : | : : 2 + : : | : : 1 + : : | : : 0 +---+---+---+---+---+--> x 0 1 2 3 4 5 The slope of the line joining (3,4) and (4,6) is the difference in y coordinates divided by the difference in x coordinates, or "rise" (step height) over "run" (step width). The rise is 2 and the run is 1. The slope is therefore 2/1, or 2. I'll do the next one without a graph. What is the slope of the line through (18,-4) and (6,-10)? The rise (difference in y) is (-10) - (-4) = -10 + 4 = -6 The run (difference in x) is 6 - 18 = -12 The slope is rise/run = (-6)/(-12) = 1/2 We could just as well have switched the two points; the slope would come out the same: (6,-10) and (18,-4). rise = (-4) - (-10) = -4 + 10 = 6 run = 18 - 6 = 12 slope = rise/run = 6/12 = 1/2 Now let's do one of the last two problems. What is r such that the slope of the line through (9,r) and (6,3) is m = -1/3? I'll do it graphically first so you can get the idea, then I'll do it numerically. y \ | \ 3 + (6,3) X | | -1| \ | 2 + +-----------O (9,r) | : 3 | \ 1 + : | | : | 0 +---+---+---+---+---+---+---+---+---+---+--> x 0 1 2 3 4 5 6 7 8 9 10 The point (6,3) is marked X. I then drew a line with slope -1/3 through this point: the rise is -1 (it falls instead of rising) and the run is 3. The other point (9,r) has x-coordinate 9, so it is on the vertical line through x = 9. Where the two lines intersect, at O, is the point we're looking for; its y-coordinate is r. Can you see what r is? Now I'll do it numerically so we can be sure we have the exact answer. Let's switch the points: (6,3) and (9,r). The rise is r - 3 and the run is 9 - 6 = 3. Therefore the slope is (r-3)/3. If the slope is -1/3, we have the equation (r-3)/3 = -1/3 What is r? I will leave this to you to solve. I hope you get the idea now - if it's still confusing, we can try some more. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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