- 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:
Next, divide both sides of the equation by 8 and your slope-intercept form will be
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:
<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:
Next, add the numerators together:
<u>Your final answer is -22/5.</u>