Question 217928: Find the slope if it exists of the line containing the pair of points:
(4,5) and (8,-3)
Found 3 solutions by rfer, RAY100, drj:
Answer by rfer(16322)   (Show Source):
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! slope =m = (y2-y2)/(x2-x1)
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for (4,5) and (8,-3)
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m= (5-(-3))/(4-8) = 8/-4= -2,,,,,answer
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if we reversed the coordinates, the answer remains the same,,,
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m=(-3-5)/(8-4) = -8/4 = -2
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Note, it is very easy to make a rough sketch, showing the points, and the rt triangle showing ,,,,delta x, and delta y.
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Just remember,,slope is rise/run,,,or delta y/ delta x
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positive slope rises to rt,,negative drops to right,,,
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Answer by drj(1380)  (Show Source):
You can put this solution on YOUR website! Find the slope if it exists of the line containing the pair of points:
(4,5) and (8,-3)
However, here are the steps showing you how you can check your work with one of the points.
Step 1. The slope of the line m is given as
where for our example is x1=4, y1=5, x2=8 and y2=-3 (think of  ). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.
Step 2. Substituting the above values in the slope equation gives
Step 3. The slope is calculated as -2 or m=-2
Step 4. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (4,5). Letting y=y2 and x=x2 and substituting m=-2 in the slope equation given as,
Step 5. Multiply both sides of equation by x-4 to get rid of denomination found on the right side of the equation
Step 6. Now simplify and put the above equation into slope-intercept form.
Add 5 to both sides of the equation
 ANSWER in slope-intercept form. m=-2 and y-intercept=13
Step 7. See if the other point (8,-3) or x=8 and y=-3 satisfies this equation
 which is a true statement
 So the point (8,-3) satisfies the equation and is on the line. In other words, you can use the other point to check your work.
Note; above equation can be also be transform into standard form as
See graph below to check the above steps and note the slope and the y-intercept at x=0
I hope the above steps were helpful.
And good luck in your studies!
For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Respectfully,
Dr J
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