Question
Graph this line:
y+4=
–
1
5
(x+10)
Click to select points on the graph.
y+4=
–
1
5
(x+10)
Click to select points on the graph.
Answers
GPT-4o mini
To graph the equation given in the format \( y + 4 = -\frac{1}{5}(x + 10) \), we'll first rearrange it to slope-intercept form, \( y = mx + b \).
1. Start by distributing the right-hand side:
\[ y + 4 = -\frac{1}{5}(x + 10) \]
\[ y + 4 = -\frac{1}{5}x - 2 \]
2. Next, isolate \( y \) by subtracting 4 from both sides:
\[ y = -\frac{1}{5}x - 2 - 4 \]
\[ y = -\frac{1}{5}x - 6 \]
Now, we know that the slope \( m \) is \( -\frac{1}{5} \) and the y-intercept \( b \) is \( -6 \).
### Steps to graph the equation:
1. **Plot the y-intercept**: Start at the y-axis (where \( x = 0 \)). The y-intercept is at \( (0, -6) \).
2. **Use the slope to find another point**: The slope \( -\frac{1}{5} \) means that for every 5 units you move to the right (positive x-direction), you move 1 unit down (negative y-direction).
- Starting from the point \( (0, -6) \), move 5 units to the right to \( (5, -6) \) and then down 1 unit to \( (5, -7) \).
3. **Draw the line**: Connect these points with a straight line, extending both directions.
### Points to plot:
- \( (0, -6) \)
- \( (5, -7) \)
You can continue plotting points by choosing different values for \( x \) to find corresponding \( y \)-values using the equation \( y = -\frac{1}{5}x - 6 \).
You can plot as many points as needed to ensure your line is accurate. Let me know if you need further assistance!
1. Start by distributing the right-hand side:
\[ y + 4 = -\frac{1}{5}(x + 10) \]
\[ y + 4 = -\frac{1}{5}x - 2 \]
2. Next, isolate \( y \) by subtracting 4 from both sides:
\[ y = -\frac{1}{5}x - 2 - 4 \]
\[ y = -\frac{1}{5}x - 6 \]
Now, we know that the slope \( m \) is \( -\frac{1}{5} \) and the y-intercept \( b \) is \( -6 \).
### Steps to graph the equation:
1. **Plot the y-intercept**: Start at the y-axis (where \( x = 0 \)). The y-intercept is at \( (0, -6) \).
2. **Use the slope to find another point**: The slope \( -\frac{1}{5} \) means that for every 5 units you move to the right (positive x-direction), you move 1 unit down (negative y-direction).
- Starting from the point \( (0, -6) \), move 5 units to the right to \( (5, -6) \) and then down 1 unit to \( (5, -7) \).
3. **Draw the line**: Connect these points with a straight line, extending both directions.
### Points to plot:
- \( (0, -6) \)
- \( (5, -7) \)
You can continue plotting points by choosing different values for \( x \) to find corresponding \( y \)-values using the equation \( y = -\frac{1}{5}x - 6 \).
You can plot as many points as needed to ensure your line is accurate. Let me know if you need further assistance!