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Question 1200271: Find the equation of the line through the points (-5,3) and (-6,-1). Express the equation of the line in slope=intercept form, y=mx+b.
So I know y2-y1/x2-x1 so I did that (-1-3/-6-(-5)=(-4/1)
y=mx+b so 3=-(4/1)(-5)+b
solved for that to get b=-17
y=(-4/1)x-17
Found 4 solutions by josgarithmetic, greenestamps, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Your basic process is fine. But you got off on the wrong foot by calculating the slope incorrectly.
You calculated the slope as -4 and then used the point (-5,3) to find your equation y=-4x-17. That part of your process was fine; but the slope you found was not right. If you had also checked the point (-6,-1) with your slope of -4, you would have seen that something was wrong.
I have seen probably hundreds of cases where a student calculated the slope of a line through two given points incorrectly by plugging the wrong numbers in the slope formula, or by making arithmetic errors in the calculation (as you did: -6-(-5) is -1, not 1).
I would recommend NOT using the slope formula but rather drawing a quick sketch -- on paper, or at least in your mind -- of the two given points. In your example, even a very rough sketch would show that the line goes up as you move to the right, which means the slope is positive, so the slope of -4 you calculated could not be right.
So IF you use the slope formula to calculate the slope, then at least use a sketch to see if the slope you calculate is reasonable.
But using the sketch to find the rise and run -- and thus to determine the slope -- is much easier with a sketch than with a formula. A quick sketch of the two given points shows the run (from -6 to -5) is 1 and the rise (from -1 to 3) is 4, so the slope is -4/-1 = 4, not -4/1 = -4.
Then, with the correct slope of 4 instead of -4 and EITHER of the two points, you can come up with the correct equation y = 4x+23.
So here again is my recommendation:
On a few examples, try calculating slopes by drawing a rough sketch and using the rise and run that you get from the sketch. But if that doesn't "work" for you, then use the slope formula -- but make a quick sketch to see if the slope you calculate using the formula is reasonable.
Answer by math_tutor2020(3817) (Show Source):
Answer by ikleyn(52781)  (Show Source):
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