To graph the linear equation [tex]\( -x - 2y = 8 \)[/tex], we need to find at least three points that satisfy this equation. Here is a detailed, step-by-step solution:
1. Choose a value for [tex]\( x \)[/tex] and solve for [tex]\( y \)[/tex]:
- Let's start with [tex]\( x = 0 \)[/tex]:
[tex]\[
-0 - 2y = 8 \implies -2y = 8 \implies y = -4
\][/tex]
So the first point is [tex]\( (0, -4) \)[/tex].
2. Choose another value for [tex]\( x \)[/tex] and solve for [tex]\( y \)[/tex]:
- Now, let's use [tex]\( x = 2 \)[/tex]:
[tex]\[
-2 - 2y = 8 \implies -2y = 10 \implies y = -5
\][/tex]
So the second point is [tex]\( (2, -5) \)[/tex].
3. Choose a third value for [tex]\( x \)[/tex] and solve for [tex]\( y \)[/tex]:
- Finally, let's take [tex]\( x = -2 \)[/tex]:
[tex]\[
2 - 2y = 8 \implies -2y = 6 \implies y = -3
\][/tex]
So the third point is [tex]\( (-2, -3) \)[/tex].
Now that we have our three points:
- [tex]\( (0, -4) \)[/tex]
- [tex]\( (2, -5) \)[/tex]
- [tex]\( (-2, -3) \)[/tex]
You can plot these points on a graph. Draw the graph of the equation by:
- Plotting the point [tex]\( (0, -4) \)[/tex]
- Plotting the point [tex]\( (2, -5) \)[/tex]
- Plotting the point [tex]\( (-2, -3) \)[/tex]
Then draw a line through these three points to represent the linear equation [tex]\( -x - 2y = 8 \)[/tex]. This line will extend infinitely in both directions, but you only need to mark these specific points to clearly identify the linear relationship.
Once all points are plotted accurately, connect them with a straight line to complete the graph.
