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

Answer 1

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:

1. **Line 2 has the biggest y-intercept** - False (Line 3 has the biggest y-intercept of 19).
2. **Line 1 has the greatest slope** - False (Line 3 has a slope of 3, which is greater than 2).
3. **Line 3 has the greatest slope** - True (Line 3 has the greatest slope of 3).
4. **Line 1 has the biggest y-intercept** - False (Line 3 has the biggest y-intercept).
5. **Line 2 has an increasing graph** - False (Line 2 has a negative slope).
6. **Line 3 has a decreasing graph** - False (Line 3 has a positive slope).

The true statement is:
**Line 3 has the greatest slope.**