Question

The equation of Line 1: 2x−4y=16


The equation of Line 2: y=−34x−3


The equation of Line 3: y−5=−2(x+1)


Which statement is true?

(2 points)
Responses

Line 3 has the least steep slope.
Line 3 has the least steep slope.

Line 1 has the steepest slope.
Line 1 has the steepest slope.

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

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

Answer 1

To analyze the statements regarding the slopes and intercepts of the given lines, we will rewrite each line in slope-intercept form (y = mx + b) and identify their slopes and y-intercepts.

**Line 1: 2x - 4y = 16**

First, rearranging to get y alone:
\[
-4y = -2x + 16 \\
y = \frac{1}{2}x - 4
\]
- Slope (m) = 1/2
- Y-intercept (b) = -4

**Line 2: y = -\frac{3}{4}x - 3**

This line is already in slope-intercept form.
- Slope (m) = -3/4
- Y-intercept (b) = -3

**Line 3: y - 5 = -2(x + 1)**

Expanding this:
\[
y - 5 = -2x - 2 \\
y = -2x + 3
\]
- Slope (m) = -2
- Y-intercept (b) = 3

**Comparison of the slopes:**
- Line 1: Slope = 1/2
- Line 2: Slope = -3/4
- Line 3: Slope = -2

The slope value indicates steepness. A positive slope is less steep than a negative slope with a greater absolute value; thus:
- Line 1 has the least steep slope (1/2).
- Line 2 is steeper than Line 1 (since -3/4 is more negative).
- Line 3 is the steepest (the most negative slope of -2).

**Comparison of the y-intercepts:**
- Line 1: Y-intercept = -4
- Line 2: Y-intercept = -3
- Line 3: Y-intercept = 3

The greatest y-intercept is 3 from Line 3.

Now we can evaluate the statements based on our analysis:

1. **Line 3 has the least steep slope.** (False, Line 1 has the least steep slope)
2. **Line 1 has the steepest slope.** (False, Line 3 has the steepest slope)
3. **Line 1 has the biggest y-intercept.** (False, Line 3 has the biggest y-intercept)
4. **Line 3 has a decreasing graph.** (True, because slope is -2)
5. **Line 2 has an increasing graph.** (False, slope is -3/4, so this line is decreasing.)
6. **Line 2 has the biggest y-intercept.** (False, Line 3 has the biggest y-intercept)

**Conclusion: The true statement is: Line 3 has a decreasing graph.**