To graph the line given by the equation \(y + 4 = \frac{1}{4}(x - 1)\), we first need to rewrite it in slope-intercept form \(y = mx + b\).
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Start with the given equation: \[ y + 4 = \frac{1}{4}(x - 1) \]
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Distribute the \(\frac{1}{4}\): \[ y + 4 = \frac{1}{4}x - \frac{1}{4} \]
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Isolate \(y\) by subtracting 4 from both sides: \[ y = \frac{1}{4}x - \frac{1}{4} - 4 \]
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Combine constants on the right side: \[ y = \frac{1}{4}x - \frac{1}{4} - \frac{16}{4} \] \[ y = \frac{1}{4}x - \frac{17}{4} \]
Now we have the equation of the line in slope-intercept form:
\[ y = \frac{1}{4}x - \frac{17}{4} \]
Identifying Points
The slope \(m\) is \(\frac{1}{4}\), and the y-intercept \(b\) is \(-\frac{17}{4}\), which is approximately \(-4.25\).
Finding Points
We can choose some x-values to find corresponding y-values to plot points on the graph:
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For \(x = 0\): \[ y = \frac{1}{4}(0) - \frac{17}{4} = -\frac{17}{4} \approx -4.25 \quad \text{(Point: (0, -4.25))} \]
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For \(x = 4\): \[ y = \frac{1}{4}(4) - \frac{17}{4} = 1 - \frac{17}{4} = 1 - 4.25 = -3.25 \quad \text{(Point: (4, -3.25))} \]
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For \(x = 8\): \[ y = \frac{1}{4}(8) - \frac{17}{4} = 2 - \frac{17}{4} = 2 - 4.25 = -2.25 \quad \text{(Point: (8, -2.25))} \]
Graphing the Line
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Plot the points found:
- (0, -4.25)
- (4, -3.25)
- (8, -2.25)
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Draw a straight line through these points.
This visual representation will show a line with a positive slope that rises gently as x increases, intersecting the y-axis below the origin.