- Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept
So firstly, remember that <u>perpendicular lines have slopes that are negative reciprocals to each other.</u> To find the slope of L1, the easiest method is to convert it into slope-intercept form.
Firstly, subtract 5x on both sides of the equation: ![8y=-5x-9](https://tex.z-dn.net/?f=8y%3D-5x-9)
Next, divide both sides of the equation by 8 and your slope-intercept form will be ![y=-\frac{5}{8}x-\frac{9}{8}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B8%7Dx-%5Cfrac%7B9%7D%7B8%7D)
Now looking at this equation, the slope appears to be -5/8 for L1. <u>Since L2 is perpendicular, this means that the slope of L2 is 8/5.</u>
Next, to find the y-intercept, put the slope into the m variable and put (10,10) into the x and y placeholders to solve for b as such:
![10=\frac{8}{5}*10+b\\10=16+b\\-6=b](https://tex.z-dn.net/?f=10%3D%5Cfrac%7B8%7D%7B5%7D%2A10%2Bb%5C%5C10%3D16%2Bb%5C%5C-6%3Db)
<u>Putting it together, your equation is
, with m = 8/5 and b = -6.</u>
Next, to find the sum you first need to convert -6 so that it has a denominator of 5. To do this, multiply -6 by 5/5 as such:
![-\frac{6}{1}\times\frac{5}{5}=-\frac{30}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B6%7D%7B1%7D%5Ctimes%5Cfrac%7B5%7D%7B5%7D%3D-%5Cfrac%7B30%7D%7B5%7D)
Next, add the numerators together:
![-\frac{30}{5}+\frac{8}{5}=-\frac{22}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B30%7D%7B5%7D%2B%5Cfrac%7B8%7D%7B5%7D%3D-%5Cfrac%7B22%7D%7B5%7D)
<u>Your final answer is -22/5.</u>