Question

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.

Answer 1

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?

Answer 2

y=5/4x+11/2

Answer 3

I was going more for the concept than the answer, 14yamaka.

Answer 4

c=y-mx

Answer 5

sorry :S

Answer 6

\[y-y_1 = m(x-x_1) \] if I remember from A-Levels lol. So we have
\[y-8 = \frac{5}{4}(x-2)\]
\[y = \frac{5}{4}x +8- \frac{10}{4}\]
\[y=\frac{5}{4}x +\frac{11}{2}\]

Answer 7

Thanks, guys. Those pesky fractions. Looks like I am really going to have to brush up on my basics. :(

Answer 8

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...