Question

Graph this line:
y–4=
–
1
5
(x+10)
Click to select points on the graph.

Answer 1

To graph the line given by the equation \( y - 4 = -\frac{1}{5}(x + 10) \), we first want to rewrite it in slope-intercept form (i.e., \( y = mx + b \)).

1. Start with the equation:
\[
y - 4 = -\frac{1}{5}(x + 10)
\]

2. Distribute the \(-\frac{1}{5}\):
\[
y - 4 = -\frac{1}{5}x - 2
\]

3. Add 4 to both sides:
\[
y = -\frac{1}{5}x - 2 + 4
\]
\[
y = -\frac{1}{5}x + 2
\]

Now we have the equation in slope-intercept form, where the slope \( m = -\frac{1}{5} \) and the y-intercept \( b = 2 \).

### Finding Points on the Line

To graph the line, we can use the y-intercept and find another point using the slope:

1. **Y-Intercept Point**: The y-intercept is at \( (0, 2) \).

2. **Using the Slope**: The slope of \(-\frac{1}{5}\) means that for every 5 units you move to the right (positive direction on the x-axis), you move 1 unit down (negative direction on the y-axis).
- Starting from the y-intercept \( (0, 2) \):
- Move 5 units to the right to \( (5, 2) \).
- Move down 1 unit to \( (5, 1) \).

Thus, we can plot the points:
- \( (0, 2) \)
- \( (5, 1) \)

### Graphing the Line

1. Plot the points \( (0, 2) \) and \( (5, 1) \).
2. Draw a straight line through these points extended in both directions.

If you have graphing software or paper, you can now perform these steps to see the line represented graphically!