Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Sure, let's graph the equation [tex]\( -8x - y = 8 \)[/tex]. To do this, we'll follow these steps:
1. Rearrange the equation into slope-intercept form:
The given equation is [tex]\( -8x - y = 8 \)[/tex]. Rearrange it to solve for [tex]\( y \)[/tex]:
[tex]\[ -y = 8 + 8x \implies y = -8x - 8. \][/tex]
Here, you have it in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Slope ([tex]\( m \)[/tex]) = [tex]\(-8\)[/tex]
- Y-intercept ([tex]\( b \)[/tex]) = [tex]\(-8\)[/tex]
2. Find the x-intercept:
To find the x-intercept, set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = -8x - 8 \implies 8x = -8 \implies x = -1. \][/tex]
Therefore, the x-intercept is at [tex]\( (-1, 0) \)[/tex].
3. Identify key points:
- The y-intercept is [tex]\( (0, -8) \)[/tex].
- The x-intercept is [tex]\( (-1, 0) \)[/tex].
4. Plot the intercepts:
On a coordinate plane, plot the points [tex]\( (0, -8) \)[/tex] and [tex]\( (-1, 0) \)[/tex].
5. Draw the line:
With the points [tex]\( (0, -8) \)[/tex] and [tex]\( (-1, 0) \)[/tex] plotted, draw a straight line through these points. This line represents the graph of the equation [tex]\( -8x - y = 8 \)[/tex].
### Summary:
- The slope of the line is [tex]\(-8\)[/tex], meaning the line is very steep, going downwards from left to right.
- The y-intercept is at the point [tex]\( (0, -8) \)[/tex].
- The x-intercept is at the point [tex]\( (-1, 0) \)[/tex].
### Sketch:
Your graph should look like this:
[tex]\[ \begin{array}{c|c} x & y \\ \hline -2 & 8 \\ -1 & 0 \\ 0 & -8 \\ 1 & -16 \\ \end{array} \][/tex]
By plotting these points and drawing a straight line through them, you can visualize the graph of [tex]\( -8x - y = 8 \)[/tex].
Here's how our key points would position on the graph:
- Point [tex]\((-1, 0)\)[/tex] on the x-axis (x-intercept)
- Point [tex]\( (0, -8) \)[/tex] on the y-axis (y-intercept)
Using these points helps in accurately drawing the line, showing a steep descent due to the negative slope of -8.
1. Rearrange the equation into slope-intercept form:
The given equation is [tex]\( -8x - y = 8 \)[/tex]. Rearrange it to solve for [tex]\( y \)[/tex]:
[tex]\[ -y = 8 + 8x \implies y = -8x - 8. \][/tex]
Here, you have it in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Slope ([tex]\( m \)[/tex]) = [tex]\(-8\)[/tex]
- Y-intercept ([tex]\( b \)[/tex]) = [tex]\(-8\)[/tex]
2. Find the x-intercept:
To find the x-intercept, set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = -8x - 8 \implies 8x = -8 \implies x = -1. \][/tex]
Therefore, the x-intercept is at [tex]\( (-1, 0) \)[/tex].
3. Identify key points:
- The y-intercept is [tex]\( (0, -8) \)[/tex].
- The x-intercept is [tex]\( (-1, 0) \)[/tex].
4. Plot the intercepts:
On a coordinate plane, plot the points [tex]\( (0, -8) \)[/tex] and [tex]\( (-1, 0) \)[/tex].
5. Draw the line:
With the points [tex]\( (0, -8) \)[/tex] and [tex]\( (-1, 0) \)[/tex] plotted, draw a straight line through these points. This line represents the graph of the equation [tex]\( -8x - y = 8 \)[/tex].
### Summary:
- The slope of the line is [tex]\(-8\)[/tex], meaning the line is very steep, going downwards from left to right.
- The y-intercept is at the point [tex]\( (0, -8) \)[/tex].
- The x-intercept is at the point [tex]\( (-1, 0) \)[/tex].
### Sketch:
Your graph should look like this:
[tex]\[ \begin{array}{c|c} x & y \\ \hline -2 & 8 \\ -1 & 0 \\ 0 & -8 \\ 1 & -16 \\ \end{array} \][/tex]
By plotting these points and drawing a straight line through them, you can visualize the graph of [tex]\( -8x - y = 8 \)[/tex].
Here's how our key points would position on the graph:
- Point [tex]\((-1, 0)\)[/tex] on the x-axis (x-intercept)
- Point [tex]\( (0, -8) \)[/tex] on the y-axis (y-intercept)
Using these points helps in accurately drawing the line, showing a steep descent due to the negative slope of -8.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
