<h3>Answer:</h3>
Y = 3X + 12
<h3>Explanation:</h3>
You are given several points on the line, so you can use a couple of them to find the slope, then write the equation in point-slope form and rearrange it to the desired form.
... slope = (change in Y)/(change in X)
Using the first two points, this is ...
... slope = (69 -51)/(19 -13) = 18/6 = 3
<em>Point-Slope Form</em>
The point-slope form of the equation of a line is usually written ...
... y -y1 = m(x -x1) . . . . . . where m = slope, (x1, y1) = point
This can be put into a y= form by adding y1:
... y = m(x -x1) +y1
<em>Your Equation</em>
Filling in m=3, (x1, y1) = (13, 51), the equation becomes
... y = 3(x -13) +51
... y = 3x -39 +51 . . . . . eliminate parentheses
... y = 3x +12 . . . . . . . . . simplify to slope-intercept form
_____
<em>Alternate Solution</em>
Having found the slope to be 3, you can write the slope-intercept form and fill in what you know.
... y = mx + b . . . . . slope-intercept form
... 51 = 3·13 +b . . . . slope-intercept form with slope and first point filled in
... 51 -39 = b = 12 . . . . equation solved for <em>b</em> by subtracting 39
Now you know that the equation is
... y = 3x +12
![\frac{d}{dx}[y]= \frac{d}{dx}[ln(sinh(2x))]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5By%5D%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bln%28sinh%282x%29%29%5D)
![\frac{dy}{dx} = \frac{1}{sinh(2x) } * \frac{d}{dx}[sinh(2x)]](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7Bsinh%282x%29%20%7D%20%2A%20%20%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bsinh%282x%29%5D)
![\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) * \frac{d}{dx}[2x]](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7Bsinh%282x%29%20%7D%20%2A%20cosh%282x%29%20%2A%20%20%5Cfrac%7Bd%7D%7Bdx%7D%5B2x%5D%20)
