Answer:
First, let's start with y = x + 5.
To graph this equation, we can use a table of values. We'll choose a few values of x, and then plug them into the equation to find the corresponding values of y.
x | y
--|---
-5 | 0
-4 | 1
-3 | 2
-2 | 3
-1 | 4
0 | 5
1 | 6
2 | 7
3 | 8
4 | 9
5 | 10
Now, we can plot these points on a graph and connect them with a straight line.
```
| *
10|
| *
| *
| *
|*
| -------------
| -5 -4 -3 -2 -1 0 1 2 3 4 5
```
This is the graph of y = x + 5.
Next, let's look at y = -(x + 5).
This equation is similar to the first one, but with a negative sign in front of the parentheses. This means that the graph will be a mirror image of the first one, reflected across the y-axis.
So, we already know some of the points on this graph. If we take the points from the first graph and flip them horizontally (i.e. change the sign of the x-coordinate), we'll get the points for the second graph.
x | y
--|---
5 | 0
4 | -1
3 | -2
2 | -3
1 | -4
0 | -5
-1 | -6
-2 | -7
-3 | -8
-4 | -9
-5 | -10
Plotting these points on a graph and connecting them with a straight line, we get:
```
|*
10| *
| *
| *
| *
| *
| *
| *
|---------------
| -5 -4 -3 -2 -1 0 1 2 3 4 5
```
This is the graph of y = -(x + 5).
Finally, let's look at y = |x + 5|.
This equation involves absolute value, which means that the graph will be "V"-shaped. The vertex of the "V" will be at x = -5.
To find some points on this graph, we can again use a table of values. We'll choose some values of x, and then plug them into the equation, being careful to take the absolute value of the result.
x | y
--|---
-10 | 5
-5 | 0
0 | 5
5 | 10
10 | 15
Now, we can plot these points on a graph and connect them to form a "V" shape.
```
| *
15| *
| *
| *
| *
| *
|-------------
|-10 -5 0 5 10
```
This is the graph of y = |x + 5|.