To analyze the three lines, we will first convert the equations into slope-intercept form (y = mx + b) to find their slopes and y-intercepts.
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Line 1: \(2x - 4y = 16\) \[ -4y = -2x + 16 \ y = \frac{1}{2}x - 4 \]
- Slope (m) = \( \frac{1}{2} \)
- Y-intercept (b) = -4
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Line 2: \(y = -\frac{3}{4}x - 4\)
- Slope (m) = \(-\frac{3}{4}\)
- Y-intercept (b) = -4
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Line 3: \(y - 5 = -2(x + 1)\) \[ y - 5 = -2x - 2 \ y = -2x + 3 \]
- Slope (m) = -2
- Y-intercept (b) = 3
Now, let's summarize the slopes and y-intercepts:
- Line 1: Slope = \( \frac{1}{2} \), Y-intercept = -4
- Line 2: Slope = \(-\frac{3}{4}\), Y-intercept = -4
- Line 3: Slope = -2, Y-intercept = 3
Now, let's evaluate each of the statements:
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Line 3 has the least steep slope.
- Slope of Line 3 (-2) is more steep than Line 1 \(\left(\frac{1}{2}\right)\) and Line 2 \(-\frac{3}{4}\). False
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Line 2 has an increasing graph.
- The slope of Line 2 is negative \(-\frac{3}{4}\), indicating a decreasing graph. False
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Line 1 has the steepest slope.
- Slope of Line 1 is \(\frac{1}{2}\), while Line 2 is \(-\frac{3}{4}\) (less steep than Line 1), and Line 3 has slope -2 (also less steep). Line 1 is not the steepest. False
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Line 2 has the biggest y-intercept.
- The y-intercepts of Line 1 = -4, Line 2 = -4, and Line 3 = 3. Line 3 has the largest y-intercept. False
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Line 1 has the biggest y-intercept.
- As stated above, Line 3 has the biggest y-intercept (3), while Lines 1 and 2 both have -4. False
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Line 3 has a decreasing graph.
- The slope of Line 3 is -2, which is negative, indicating a decreasing graph. True
Thus, the only true statement is Line 3 has a decreasing graph.
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