Certainly! To graph the line given by the equation [tex]\( -2x + y = -6 \)[/tex], follow these steps:
### Step 1: Rewrite the Equation in Slope-Intercept Form
The given equation of the line is:
[tex]\[ -2x + y = -6 \][/tex]
To write it in the slope-intercept form [tex]\( y = mx + b \)[/tex], solve for [tex]\( y \)[/tex]:
[tex]\[ y = 2x - 6 \][/tex]
Here, the slope ([tex]\( m \)[/tex]) is 2, and the y-intercept ([tex]\( b \)[/tex]) is -6.
### Step 2: Identify Key Points on the Line
Y-Intercept: This is where the line crosses the y-axis. When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) - 6 = -6 \][/tex]
So, the y-intercept is (0, -6).
X-Intercept: This is where the line crosses the x-axis. When [tex]\( y = 0 \)[/tex]:
[tex]\[ 0 = 2x - 6 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 6 \][/tex]
[tex]\[ x = 3 \][/tex]
So, the x-intercept is (3, 0).
### Step 3: Plot the Intercepts
- Plot (0, -6) on the y-axis.
- Plot (3, 0) on the x-axis.
### Step 4: Plot Another Point for Accuracy (Optional)
Let's choose [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) - 6 = 2 - 6 = -4 \][/tex]
So, another point on the line is (1, -4).
### Step 5: Draw the Line
- Use a ruler to draw a straight line through the points (0, -6) and (3, 0).
- Verify that the line also passes through the point (1, -4) for accuracy.
### Step 6: Label the Graph
- Label the x-axis and y-axis.
- Mark and label the intercepts and any additional plotted points.
- Optionally, add a title such as "Graph of the line [tex]\( -2x + y = -6 \)[/tex]".
By following these steps, you will be able to accurately graph the line. Here is a visual representation for clarity:
```
|
5 -|
|
3 -| x
|
1 -|
|
-1-|
|
-3-|
|
-5-|
|
-7-|
---------------------
-2 -1 0 1 2 3
```
- Point A = (0, -6) [Y-Intercept]
- Point B = (3, 0) [X-Intercept]
- Point C = (1, -4) [An additional point for accuracy]
Draw a line through these points and extend it across the graph. That's the desired result for the line [tex]\( -2x + y = -6 \)[/tex].
