Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
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].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
