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.
