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Sketch the graphs of the following equations. y=x +5, y = -(x + 5), and y=|x +5|​

2 Answers

0 votes

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|.

User Jaro
by
7.6k points
4 votes

Answer: below

Explanation:

The first equation y = x + 5 is the equation of a straight line with slope 1 and y-intercept 5. We can plot this line by starting at the point (0, 5) and then moving up one unit for every one unit to the right.

The second equation y = -(x + 5) is also the equation of a straight line, but with slope -1 and y-intercept -5. We can plot this line by starting at the point (0, -5) and then moving down one unit for every one unit to the right.

The third equation y = |x + 5| is the equation of a V-shaped graph, or an absolute value function, centered at x = -5. We can plot this graph by first plotting the portion of the graph for x < -5, which is given by y = -(x + 5). Then, we can plot the portion of the graph for x > -5, which is given by y = x + 5. Finally, we can connect these two portions of the graph at x = -5 by drawing a vertical line segment from (-5, 0) to (-5, 10).

User Tatiana Racheva
by
8.5k points

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