To graph the linear equation [tex]\( -x - 2y = -10 \)[/tex], let's first simplify it to make it easier to work with. We can rewrite the equation in the form [tex]\( ax + by = c \)[/tex], which is known as the standard form of a linear equation.
Starting with:
[tex]\[ -x - 2y = -10 \][/tex]
We can multiply every term by [tex]\(-1\)[/tex] to get:
[tex]\[ x + 2y = 10 \][/tex]
Next, we'll find three points to plot on the graph by choosing convenient values for [tex]\( x \)[/tex] or [tex]\( y \)[/tex] and solving for the corresponding variable.
### Point 1:
Let's choose [tex]\( x = 0 \)[/tex]:
[tex]\[ 0 + 2y = 10 \][/tex]
[tex]\[ 2y = 10 \][/tex]
[tex]\[ y = 5 \][/tex]
So, the first point is [tex]\( (0, 5) \)[/tex].
### Point 2:
Now, let's choose [tex]\( x = 2 \)[/tex]:
[tex]\[ 2 + 2y = 10 \][/tex]
[tex]\[ 2y = 10 - 2 \][/tex]
[tex]\[ 2y = 8 \][/tex]
[tex]\[ y = 4 \][/tex]
So, the second point is [tex]\( (2, 4) \)[/tex].
### Point 3:
Finally, let's choose [tex]\( y = 0 \)[/tex]:
[tex]\[ x + 2(0) = 10 \][/tex]
[tex]\[ x = 10 \][/tex]
So, the third point is [tex]\( (10, 0) \)[/tex].
### Summary of Points:
- [tex]\( (0, 5) \)[/tex]
- [tex]\( (2, 4) \)[/tex]
- [tex]\( (10, 0) \)[/tex]
### Plotting the Points:
1. Plot the point [tex]\( (0, 5) \)[/tex] on the graph. This is where the line crosses the y-axis.
2. Plot the point [tex]\( (2, 4) \)[/tex] on the graph.
3. Plot the point [tex]\( (10, 0) \)[/tex] on the graph. This is where the line crosses the x-axis.
### Drawing the Line:
Once the points are plotted, draw a straight line passing through all three points. This line represents the graph of the equation [tex]\( -x - 2y = -10 \)[/tex] or equivalently [tex]\( x + 2y = 10 \)[/tex].
This line is the visual representation of all solutions to the given equation.
