Question 171419


{{{8x-5y=9}}} Start with the first equation.



{{{-5y=9-8x}}} Subtract {{{8x}}} from both sides.



{{{-5y=-8x+9}}} Rearrange the terms.



{{{y=(-8x+9)/(-5)}}} Divide both sides by {{{-5}}} to isolate y.



{{{y=((-8)/(-5))x+(9)/(-5)}}} Break up the fraction.



{{{y=(8/5)x-9/5}}} Reduce.



So we can see that the equation {{{y=(8/5)x-9/5}}} has a slope {{{m=8/5}}} and a y-intercept {{{b=-9/5}}}.


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{{{5x+8y=5}}} Now move onto the second equation.



{{{8y=5-5x}}} Subtract {{{5x}}} from both sides.



{{{8y=-5x+5}}} Rearrange the terms.



{{{y=(-5x+5)/(8)}}} Divide both sides by {{{8}}} to isolate y.



{{{y=((-5)/(8))x+(5)/(8)}}} Break up the fraction.



{{{y=-(5/8)x+5/8}}} Reduce.



So we can see that the equation {{{y=-(5/8)x+5/8}}} has a slope {{{m=-5/8}}} and a y-intercept {{{b=5/8}}}.



So the slope of the first line is {{{m=8/5}}} and the slope of the second line is {{{m=-5/8}}}.



Notice how the slope of the second line {{{m=-5/8}}} is simply the negative reciprocal of the slope of the first line {{{m=8/5}}}.



In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. 



So this means that {{{y=(8/5)x-9/5}}} and {{{y=-(5/8)x+5/8}}} are perpendicular lines.