To evaluate the statements about the lines, we need to analyze the slopes and y-intercepts of all three lines.
Line 1: \(4x - 2y = 16\)
Convert to slope-intercept form (y = mx + b): \[ -2y = -4x + 16 \implies y = 2x - 8 \]
- Slope (m) = 2
- y-intercept (b) = -8
Line 2: \(y = -\frac{4}{5}x + 2\)
- Slope (m) = -\(\frac{4}{5}\)
- y-intercept (b) = 2
Line 3: \(y - 4 = 3(x + 5)\)
Convert to slope-intercept form: \[ y - 4 = 3x + 15 \implies y = 3x + 19 \]
- Slope (m) = 3
- y-intercept (b) = 19
Now, let's analyze the slopes and y-intercepts:
-
Slopes:
- Line 1: Slope = 2
- Line 2: Slope = -\(\frac{4}{5} \approx -0.8\) (decreasing)
- Line 3: Slope = 3 (greatest slope)
-
y-intercepts:
- Line 1: y-intercept = -8
- Line 2: y-intercept = 2
- Line 3: y-intercept = 19 (largest y-intercept)
Now, checking each statement:
- Line 3 has the greatest slope: True (Slope = 3)
- Line 3 has a decreasing graph: False (Slope = 3, which is increasing)
- Line 2 has an increasing graph: False (Slope = -\(\frac{4}{5}\), which is decreasing)
- Line 1 has the biggest y-intercept: False (y-intercept = -8, Line 3 has the largest y-intercept)
- Line 2 has the biggest y-intercept: False (Line 3 has the largest y-intercept)
- Line 1 has the greatest slope: False (Line 3 has the greatest slope)
Final answer: The only true statement is "Line 3 has the greatest slope."