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Llana [10]
3 years ago
13

Let line L1 be the graph of 5x + 8y = -9. Line L2 is perpendicular to line L1 and passes through the point (10,10). If line L2 i

s the graph of the equation y=mx +b, then find m+b.
Mathematics
2 answers:
AleksandrR [38]3 years ago
5 0
  • 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

Next, divide both sides of the equation by 8 and your slope-intercept form will be y=-\frac{5}{8}x-\frac{9}{8}

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

<u>Putting it together, your equation is y=\frac{8}{5}x-6, 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}

Next, add the numerators together:

-\frac{30}{5}+\frac{8}{5}=-\frac{22}{5}

<u>Your final answer is -22/5.</u>

Svetradugi [14.3K]3 years ago
3 0

Answer:

-22/5.

Step-by-step explanation:

hope this helps

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