To determine which statement is true about the given lines, we first need to analyze their equations in terms of slope and y-intercept.
Line 1: The equation is given by: \[ 4x - 2y = 16 \] We can rearrange it into slope-intercept form \(y = mx + b\): \[ -2y = -4x + 16 \] \[ y = 2x - 8 \] From this, we can see that:
- Slope (\(m\)) = 2
- y-intercept (\(b\)) = -8
Line 2: The equation is already in slope-intercept form: \[ y = -\frac{4}{5}x + 2 \] From this, we find:
- Slope (\(m\)) = \(-\frac{4}{5}\) (negative, therefore decreasing)
- y-intercept (\(b\)) = 2
Line 3: The equation is given by: \[ y - 4 = 3(x + 5) \] Rearranging this into slope-intercept form: \[ y - 4 = 3x + 15 \] \[ y = 3x + 19 \] From this, we can see that:
- Slope (\(m\)) = 3
- y-intercept (\(b\)) = 19
Now, let's summarize the properties we found:
- Line 1: Slope = 2, y-intercept = -8
- Line 2: Slope = \(-\frac{4}{5}\), y-intercept = 2
- Line 3: Slope = 3, y-intercept = 19
Next, we can evaluate the statements:
- Line 2 has the biggest y-intercept - False (Line 3 has the biggest y-intercept of 19).
- Line 1 has the greatest slope - False (Line 3 has a slope of 3, which is greater than 2).
- Line 3 has the greatest slope - True (Line 3 has the greatest slope of 3).
- Line 1 has the biggest y-intercept - False (Line 3 has the biggest y-intercept).
- Line 2 has an increasing graph - False (Line 2 has a negative slope).
- Line 3 has a decreasing graph - False (Line 3 has a positive slope).
The true statement is: Line 3 has the greatest slope.
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