To graph the line [tex]\( y = \frac{1}{5} x - 6 \)[/tex], we’ll follow these steps:
### Step 1: Identify the slope and y-intercept
The equation of the line is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -6 \)[/tex].
This means the line crosses the y-axis at the point [tex]\( (0, -6) \)[/tex].
### Step 2: Find another point on the line
To draw the line, we need at least one more point. We can find this by choosing any x-value and calculating the corresponding y-value using the equation.
Let's choose [tex]\( x = 10 \)[/tex]:
[tex]\[
y = \frac{1}{5} \cdot 10 - 6 = 2 - 6 = -4
\][/tex]
So, the point [tex]\( (10, -4) \)[/tex] lies on the line.
### Step 3: Plot the points
- Plot the y-intercept [tex]\( (0, -6) \)[/tex] on the coordinate plane.
- Plot the point [tex]\( (10, -4) \)[/tex].
### Step 4: Draw the line
Draw a straight line through these two points [tex]\( (0, -6) \)[/tex] and [tex]\( (10, -4) \)[/tex].
### Optional Step: Verify with more points
To ensure accuracy, let’s calculate a few more points:
- Choose [tex]\( x = -5 \)[/tex]:
[tex]\[
y = \frac{1}{5} \cdot (-5) - 6 = -1 - 6 = -7
\][/tex]
So, the point [tex]\( (-5, -7) \)[/tex] lies on the line.
Plot this additional point [tex]\( (-5, -7) \)[/tex] to confirm the line.
### Visual Representation
- Plot the points [tex]\( (0, -6) \)[/tex], [tex]\( (10, -4) \)[/tex], and [tex]\( (-5, -7) \)[/tex].
- Draw a straight line through these points.
The line should look like this:
```
y
|
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 | • (10, -4)
2 |
1 |
- -0- - - - - - - - - - - - - - - - - x
-1 | • (-5, -7)
-2 |
-3 |
-4 |
-5 |
-6 |• (0, -6)
-7 |
-8 |
-9 |
-10 |
|
```
By connecting these points, you'll create the graph of the line [tex]\( y = \frac{1}{5} x - 6 \)[/tex].
