Question
Graph the line with the equation y, equals, minus, one quarter, x, plus, 5y=−
4
1
x+5.
4
1
x+5.
Answers
Answered by
GPT-4o mini
To graph the line represented by the equation \( y = -\frac{1}{4}x + 5 \), we can follow these steps:
1. **Identify the y-intercept**: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, when \( x = 0 \):
\[
y = -\frac{1}{4}(0) + 5 = 5
\]
So, the y-intercept is \( (0, 5) \).
2. **Identify another point**: To find another point on the line, we can choose a value for \( x \). Let’s choose \( x = 4 \):
\[
y = -\frac{1}{4}(4) + 5 = -1 + 5 = 4
\]
Thus, another point is \( (4, 4) \).
3. **Plot the points**: Plot the points \( (0, 5) \) and \( (4, 4) \) on the graph.
4. **Draw the line**: Once the points are plotted, draw a straight line through these points extending in both directions.
5. **Optional - Identify the slope**: The slope of the line is \( -\frac{1}{4} \), meaning for every 4 units you move to the right along the x-axis, you move down 1 unit on the y-axis.
This will give you the line that represents the equation \( y = -\frac{1}{4}x + 5 \).
### Summary of Points to Plot:
- Y-intercept: \( (0, 5) \)
- Point with \( x = 4 \): \( (4, 4) \)
If you want a more detailed graph, let me know!
1. **Identify the y-intercept**: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, when \( x = 0 \):
\[
y = -\frac{1}{4}(0) + 5 = 5
\]
So, the y-intercept is \( (0, 5) \).
2. **Identify another point**: To find another point on the line, we can choose a value for \( x \). Let’s choose \( x = 4 \):
\[
y = -\frac{1}{4}(4) + 5 = -1 + 5 = 4
\]
Thus, another point is \( (4, 4) \).
3. **Plot the points**: Plot the points \( (0, 5) \) and \( (4, 4) \) on the graph.
4. **Draw the line**: Once the points are plotted, draw a straight line through these points extending in both directions.
5. **Optional - Identify the slope**: The slope of the line is \( -\frac{1}{4} \), meaning for every 4 units you move to the right along the x-axis, you move down 1 unit on the y-axis.
This will give you the line that represents the equation \( y = -\frac{1}{4}x + 5 \).
### Summary of Points to Plot:
- Y-intercept: \( (0, 5) \)
- Point with \( x = 4 \): \( (4, 4) \)
If you want a more detailed graph, let me know!
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