Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Sure, let's graph the line [tex]\( y = -x - 4 \)[/tex] for the given range of [tex]\( x \)[/tex] values from -6 to 0. Here are the steps for constructing the graph:
1. Identify the Equation and Determine Key Points:
The equation provided is [tex]\( y = -x - 4 \)[/tex]. This is a linear equation, hence forms a straight line. To graph this, we need several pairs of [tex]\( (x, y) \)[/tex] points.
2. Calculate the [tex]\( y \)[/tex] Values for Given [tex]\( x \)[/tex] Range:
We need to compute [tex]\( y \)[/tex] for various [tex]\( x \)[/tex] values within the range [tex]\([-6, 0]\)[/tex]:
- For [tex]\( x = -6 \)[/tex]: [tex]\( y = -(-6) - 4 = 6 - 4 = 2 \)[/tex]
- For [tex]\( x = -5.94 \)[/tex]: [tex]\( y = -(-5.94) - 4 \approx 1.94 \)[/tex]
- For [tex]\( x = -5.88 \)[/tex]: [tex]\( y = -(-5.88) - 4 \approx 1.88 \)[/tex]
- Continue similar calculations for multiple [tex]\( x \)[/tex] values up to [tex]\( x = 0 \)[/tex].
3. List of Calculated Points:
Here’s a list of calculated points for convenience (we will use a subset of the values for clarity):
[tex]\( \begin{align*} & (-6, 2), \\ & (-5.94, 1.94), \\ & (-5.88, 1.88), \\ & \vdots \\ & (-1, -3), \\ & (-0.5, -3.5), \\ & (0, -4). \end{align*} \)[/tex]
4. Plot the Points on a Graph:
- Draw a coordinate grid with [tex]\( x \)[/tex]-axis (horizontal) ranging from -6 to 0 and [tex]\( y \)[/tex]-axis (vertical) from -4 to 2.
- Plot the points listed above:
- [tex]\( (-6, 2) \)[/tex]
- [tex]\( (-5.94, 1.94) \)[/tex]
- [tex]\( (-5.88, 1.88) \)[/tex]
- [tex]\( \vdots \)[/tex]
- [tex]\( (-1, -3) \)[/tex]
- [tex]\( (-0.5, -3.5) \)[/tex]
- [tex]\( (0, -4) \)[/tex]
5. Draw the Line:
- After all points are plotted, connect them with a straight line. Since this is a linear function, the points will form a straight line.
6. Label the Graph:
- Label the x-axis and y-axis appropriately.
- Add the equation of the line [tex]\( y = -x - 4 \)[/tex] as a title or label near the line.
Here’s how your line should appear when you plot these points and connect them:
```plaintext
y
|
2 | (-6, 2)
1 |
0 |
-1 |
-2 |
-3 |
-4 | (0, -4)
|
---------------------------------- x
-6 -5 -4 -3 -2 -1 0
```
Therefore, the graph of the equation [tex]\( y = -x - 4 \)[/tex] is a straight line that starts from point [tex]\((-6, 2)\)[/tex] and goes down to the point [tex]\((0, -4)\)[/tex].
1. Identify the Equation and Determine Key Points:
The equation provided is [tex]\( y = -x - 4 \)[/tex]. This is a linear equation, hence forms a straight line. To graph this, we need several pairs of [tex]\( (x, y) \)[/tex] points.
2. Calculate the [tex]\( y \)[/tex] Values for Given [tex]\( x \)[/tex] Range:
We need to compute [tex]\( y \)[/tex] for various [tex]\( x \)[/tex] values within the range [tex]\([-6, 0]\)[/tex]:
- For [tex]\( x = -6 \)[/tex]: [tex]\( y = -(-6) - 4 = 6 - 4 = 2 \)[/tex]
- For [tex]\( x = -5.94 \)[/tex]: [tex]\( y = -(-5.94) - 4 \approx 1.94 \)[/tex]
- For [tex]\( x = -5.88 \)[/tex]: [tex]\( y = -(-5.88) - 4 \approx 1.88 \)[/tex]
- Continue similar calculations for multiple [tex]\( x \)[/tex] values up to [tex]\( x = 0 \)[/tex].
3. List of Calculated Points:
Here’s a list of calculated points for convenience (we will use a subset of the values for clarity):
[tex]\( \begin{align*} & (-6, 2), \\ & (-5.94, 1.94), \\ & (-5.88, 1.88), \\ & \vdots \\ & (-1, -3), \\ & (-0.5, -3.5), \\ & (0, -4). \end{align*} \)[/tex]
4. Plot the Points on a Graph:
- Draw a coordinate grid with [tex]\( x \)[/tex]-axis (horizontal) ranging from -6 to 0 and [tex]\( y \)[/tex]-axis (vertical) from -4 to 2.
- Plot the points listed above:
- [tex]\( (-6, 2) \)[/tex]
- [tex]\( (-5.94, 1.94) \)[/tex]
- [tex]\( (-5.88, 1.88) \)[/tex]
- [tex]\( \vdots \)[/tex]
- [tex]\( (-1, -3) \)[/tex]
- [tex]\( (-0.5, -3.5) \)[/tex]
- [tex]\( (0, -4) \)[/tex]
5. Draw the Line:
- After all points are plotted, connect them with a straight line. Since this is a linear function, the points will form a straight line.
6. Label the Graph:
- Label the x-axis and y-axis appropriately.
- Add the equation of the line [tex]\( y = -x - 4 \)[/tex] as a title or label near the line.
Here’s how your line should appear when you plot these points and connect them:
```plaintext
y
|
2 | (-6, 2)
1 |
0 |
-1 |
-2 |
-3 |
-4 | (0, -4)
|
---------------------------------- x
-6 -5 -4 -3 -2 -1 0
```
Therefore, the graph of the equation [tex]\( y = -x - 4 \)[/tex] is a straight line that starts from point [tex]\((-6, 2)\)[/tex] and goes down to the point [tex]\((0, -4)\)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
