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Work Shown:
Solve the second equation for y to get the following
4y+x = -9
4y = -x-9
y = (-x-9)/4
y = (-x)/4-9/4
y = (-1/4)x-9/4
The equation is in y = mx+b form where m = -1/4 is the slope of this line. Note: this is not the same as the uppercase M we're after; the lowercase m is conventionally used as the general slope term.
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The slope of the second line is -1/4. Flip the fraction to get -4/1 = -4, then flip the sign to go from -4 to +4 or just 4.
This means the slope of the first line must be 4 in order for the two lines to be perpendicular. The two perpenicular slopes multiply to -1. We see that (-1/4)*(4) = -1.
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Let's solve the first equation for y
-2x + My = 5
My = 2x+5
y = (2x+5)/M
y = (2x)/M + 5/M
y = (2/M)x + 5/M
The slope here is 2/M. It must be equal to 4, so lets equate and solve for M
2/M = 4
2 = 4M
4M = 2
M = 2/4
M = 1/2
which is our final answer
