Question

Graph this line:
y+4=
1
5
(x+2)
Click to select points on the graph.

Answers

GPT-4o mini
To graph the equation given in point-slope form, we first rewrite the equation as follows:

1. Starting with the equation:
\[
y + 4 = \frac{1}{5}(x + 2)
\]

2. We can simplify this equation for easier graphing by isolating \(y\):
\[
y = \frac{1}{5}(x + 2) - 4
\]
\[
y = \frac{1}{5}x + \frac{2}{5} - 4
\]
\[
y = \frac{1}{5}x - \frac{18}{5}
\]

Now we have the slope-intercept form of the line:
\[
y = \frac{1}{5}x - \frac{18}{5}
\]

3. The slope (\(m\)) of the line is \(\frac{1}{5}\), and the y-intercept (\(b\)) is \(-\frac{18}{5}\), which is \(-3.6\).

To plot this line:

- Start at the y-intercept (0, \(-\frac{18}{5}\)) or (0, -3.6).
- Use the slope \(\frac{1}{5}\): From any point on the line, move up 1 unit and to the right 5 units to find another point.

### Example Points:
- Starting from the y-intercept (0, -3.6):
- Move up 1 unit to (5, -2.6)
- Move to (5, -3.6)

Or, you can also find a point using \(x = -5\):
- When \(x = -5\):
\[
y = \frac{1}{5}(-5) - \frac{18}{5} = -1 - \frac{18}{5} = -\frac{23}{5} = -4.6
\]
This gives another point (-5, -4.6).

### Final Graphing:
1. Plot the points (0, -3.6), (5, -2.6), and (-5, -4.6).
2. Draw a straight line through these points.

You can click and select or mark the points on your graph based on the calculations above.