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Vitek1552 [10]
3 years ago
9

What is an equation for the line that passes through the coordinates (4,5) and (8, 3)?

Mathematics
2 answers:
horsena [70]3 years ago
8 0
The equation to find the slope of a line is y2 - y1 / x2 - x1

So, what you do is take the y coordinate in your first point, which in this case is 5, and subtract it from your y coordinate in the second point, which is 3.

3 - 5 = -2
-2 / x2 - x1

Now take the x coordinate in your first point, which in this case is 4, and subtract it from the x coordinate in your second point, which is 8.

8 - 4 = 4

Now you're left with -2 / 4, which is the equation for the line that passes through the points (4,5) and (8,3)

Hope this helps!!
lapo4ka [179]3 years ago
4 0
-1/2x+7. Because x=(y2-y1)/(x2-x1)
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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
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If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

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Integrate both sides of the first equation with respect to <em>x</em> :

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Integrate both sides with respect to <em>y</em> :

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Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

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Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

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