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Bas_tet [7]
3 years ago
10

A student finds the slope of the line between (8, 17) and (1, 4). She writes 17-41-8. What mistake did she make? What is the cor

rect answer?
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
7 0

slope = (y2-y1)/(x2-x1)

m =(17-4)/(8-1)

m = 13/7

You have to keep the pairs in the same order

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Answer:

y=-\frac{2}{5}x-\frac{1}{5}

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The equation of a line is y = mx + b

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First, let's find what m is, the slope of the line.

Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.

Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.

Now, just plug the numbers into the formula for m above, like this:

m = -\frac{2}{5}

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-\frac{2}{5}x + b

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To find b, think about what your (x,y) points mean:

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Now, look at our line's equation so far: y=-\frac{2}{5}x + b. b is what we want, the --\frac{2}{5} is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!

You can use either (x,y) point you want. The answer will be the same:

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  • (2,-1). y = mx + b or -1=-\frac{2}{5} * 2 + b, or solving for b: b = 1-(-\frac{2}{5})(2). b = -\frac{1}{5}.

See! In both cases, we got the same value for b. And this completes our problem.

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8 0
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