To analyze the given lines and determine which statements are true, we need to find their slopes and y-intercepts.
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Line 1: \(2x - 4y = 16\)
- Rearranging it to slope-intercept form (\(y = mx + b\)): \[ -4y = -2x + 16 \implies y = \frac{1}{2}x - 4 \]
- Slope (\(m_1\)): \(\frac{1}{2}\)
- y-intercept (\(b_1\)): \(-4\)
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Line 2: \(y = -\frac{3}{4}x - 3\)
- Slope (\(m_2\)): \(-\frac{3}{4}\)
- y-intercept (\(b_2\)): \(-3\)
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Line 3: \(y - 5 = -2(x + 1)\)
- Distributing: \[ y - 5 = -2x - 2 \implies y = -2x + 3 \]
- Slope (\(m_3\)): \(-2\)
- y-intercept (\(b_3\)): \(3\)
Now, we can compare the slopes and y-intercepts of each line:
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Slopes:
- Line 1: \(\frac{1}{2} \approx 0.5\)
- Line 2: \(-\frac{3}{4} \approx -0.75\)
- Line 3: \(-2\)
The steepest slope corresponds to Line 1 \((\frac{1}{2})\) since it is positive and greater than the negative slopes of Lines 2 and 3.
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Y-Intercepts:
- Line 1: \(-4\)
- Line 2: \(-3\)
- Line 3: \(3\)
The largest y-intercept is from Line 3, which has a y-intercept \(3\).
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Graph Behavior:
- Line 1: increasing graph (positive slope)
- Line 2: decreasing graph (negative slope)
- Line 3: decreasing graph (steeper negative slope)
Now we can evaluate the statements:
- Line 1 has the steepest slope - True
- Line 3 has a decreased graph - True (but that was potentially meant to say "decreasing")
- Line 2 has the biggest y-intercept - False (Line 3 has the biggest y-intercept)
- Line 3 has the least steep slope - False (Line 1 has the steepest, Line 2 is less steep than Line 3)
- Line 1 has the biggest y-intercept - False (Line 3 has the biggest y-intercept)
- Line 2 has an increasing graph - False (it decreases due to the negative slope)
In conclusion, the only two true statements are:
- Line 1 has the steepest slope.
- Line 3 has a decreased (decreasing) graph.
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