# How do you graph the equation #x=10-y# by making a table and what is its domain and range?

##### 1 Answer

graph{-x+10 [-40, 40, -20, 20]}

#### Explanation:

The way I would solve this problem is simply by rearranging the equation and isolating y.

1) y = -x +10

2) Since we know this function's root is just y = -x, we can know it is going to be a straight line pointing down. However, we also have +10. What that does is that it shifts our graph UP 10.

3) Whenever finding the domain, keep in mind that 1. The denominator should not equal 0 (in this case there is no fraction and therefore no denominator). And 2. the number under a square root sign cannot be negative (which again we have no square root in this function). With these in mind, we can see that our domain is all real numbers. From negative infinity to positive infinity.

4) The range is the resulting y-values we get after substituting all the possible x-values. Since we can have all real numbers as our X-values (domain), we can conclude that our Range is also all real numbers. From negative infinity to positive infinity.

5) You can also make a table by writing the equation down:

Y = -x + 10

And then just plug in random values for x, and see what your result for Y is. So if you plug in 10 for x, your Y will become 0; therefore you have the point (10, 0) on the graph. If you plug in 5 for x, your Y will become +5, and therefore you have the point (5, 5) on the graph, and so forth. You got the idea...

Hope it helped (c: