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Explain why any equation of the form y = —x + b is its own
inverse. Use both algebraic and graphic arguments.

Sagot :

Algebraic:

Swap x and y and then solve for y to get the inverse

y = -x+b

x = -y+b

x+y = b

y = -x+b

Therefore, the equation y = -x+b is its own inverse.

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Graph:

Plot y = -x+b on the xy grid. Select whatever value you want for b. Let's say we go for b = 7. So we have y = -x+7 to plot. This line goes through (7,0) and (0,7) as the x and y intercepts respectively.

If we mirror this line over y = x, then points on y = -x+7 will end up somewhere else on this same exact line. The lines y = x and y = -x+7 are perpendicular. They intersect at a 90 degree angle.

This verifies that y = -x+7 is its own inverse, and by extension the same applies to y = -x+b where b is any real number.

See the image screenshot below. I used Desmos to graph it. GeoGebra is another useful tool I use all the time.

View image Jimthompson5910
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