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

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

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

Line 1 has the greatest slope.
Line 1 has the greatest slope.

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

Line 2 has the biggest y-intercept
Line 2 has the biggest y-intercept
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Answer 1

Let's analyze each line's equation to find the slope and y-intercept.

**Line 1: \(4x - 2y = 16\)**

Rearranging to slope-intercept form \(y = mx + b\):
\[
-2y = -4x + 16
\]
\[
y = 2x - 8
\]

- 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: \(y - 4 = 3(x + 5)\)**

First, expand this equation:
\[
y - 4 = 3x + 15
\]
\[
y = 3x + 19
\]

- Slope (m) = 3
- Y-intercept (b) = 19

---

Now, let's summarize the slopes and y-intercepts:

1. **Line 1:** Slope = 2, Y-intercept = -8
2. **Line 2:** Slope = -\(\frac{4}{5}\), Y-intercept = 2
3. **Line 3:** Slope = 3, Y-intercept = 19

Now we can evaluate each statement:

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

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