anonymous
  • anonymous
Find the equation of a line containing the given point and having the given slope. (2,8), m=5/4 y=___x+___ I'm having problems with the fractions themselves.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Using the line-slope notation, we can say that \(\Large y = mx + c\). We have x, y and m, so can we work out c?
anonymous
  • anonymous
y=5/4x+11/2
anonymous
  • anonymous
I was going more for the concept than the answer, 14yamaka.

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anonymous
  • anonymous
c=y-mx
anonymous
  • anonymous
sorry :S
anonymous
  • anonymous
\[y-y_1 = m(x-x_1) \] if I remember from A-Levels lol. So we have \[y-8 = \frac{5}{4}(x-2)\] \[y = \frac{5}{4}x +8- \frac{10}{4}\] \[y=\frac{5}{4}x +\frac{11}{2}\]
anonymous
  • anonymous
Thanks, guys. Those pesky fractions. Looks like I am really going to have to brush up on my basics. :(
anonymous
  • anonymous
The derivation of the equation I quoted comes from the general fact that \[m = \frac{y_2-y_1}{x_2-x_1}\] which can be proved easily once one knows the definition of gradient (distance up divided by distance along). We let \[(x_2,y_2)\] be an arbitrary point, and in doing this we can find the gradient of ANY line via: \[m = \frac{y-y_1}{x-x_1}\] which we rearrange to get the equation I began my last answer to...

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