Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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.

-------------------------

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
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.