## anonymous 4 years ago 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.

1. 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?

2. anonymous

y=5/4x+11/2

3. anonymous

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

4. anonymous

c=y-mx

5. anonymous

sorry :S

6. anonymous

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

7. anonymous

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

8. 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...