Question

The equation of Line 1: 4x-2y=16
The equation of Line 2: y=-4/5x+2
The equation of Line 3: y-4=3(x+5)
Which statement is true?

Line 3 has the greatest slope
Line 3 has a decreasing graph
Line 2 has an increasing graph
Line 1 has the biggest y-intercept
Line 2 has the biggest y-intercept
Line 1 has the greatest slope

Answer 1

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:**
1. **Line 3 has the greatest slope**: **True** (Slope = 3)
2. **Line 3 has a decreasing graph**: **False** (Slope = 3, which is increasing)
3. **Line 2 has an increasing graph**: **False** (Slope = -\(\frac{4}{5}\), which is decreasing)
4. **Line 1 has the biggest y-intercept**: **False** (y-intercept = -8, Line 3 has the largest y-intercept)
5. **Line 2 has the biggest y-intercept**: **False** (Line 3 has the largest y-intercept)
6. **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."**