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?

(1 point)
Responses

Line 2 has an increasing graph
Line 2 has an increasing graph

Line 3 has the greatest slope
Line 3 has the greatest slope

Line 2 has the biggest y-intercept
Line 2 has the biggest y-intercept

Line 1 has the biggest y-intercept
Line 1 has the biggest y-intercept

Line 3 has a decreasing graph
Line 3 has a decreasing graph

Line 1 has the greatest slope.

Answer 1

To evaluate which statement is true, we need to determine the slopes and y-intercepts of each line.

**Line 1: \(4x - 2y = 16\)**
We can rewrite this in slope-intercept form \(y = mx + b\):

1. Rearranging gives:
\(-2y = -4x + 16\)
\(y = 2x - 8\)

- **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: \(y - 4 = 3(x + 5)\)**
Rewrite it in slope-intercept form:

1. Expanding gives:
\(y - 4 = 3x + 15\)
\(y = 3x + 19\)

- **Slope (m)**: 3
- **Y-intercept (b)**: 19

Now we compare slopes and y-intercepts:

- **Slopes**:
- Line 1: 2
- Line 2: \(-\frac{4}{5}\) (decreasing)
- Line 3: 3 (greatest slope)

- **Y-intercepts**:
- Line 1: -8
- Line 2: 2
- Line 3: 19 (greatest y-intercept)

Now we can evaluate the statements:

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

Thus, the true statement is:

**Line 3 has the greatest slope.**