Question

Which of the following lines is parallel to the line y=14x+2
?

Option #1: y=14x+8


Option #2: 4y=x+8


Option #3: y=4x+2


Option #4: y=−4x+8


(1 point)
The line in Option #
is parallel to the given line.
Remaining Attempts : 3

Answer 1

To determine which line is parallel to the line \( y = 14x + 2 \), we need to identify the slope of this line. The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope.

In this case, the slope (m) of the line \( y = 14x + 2 \) is \( 14 \).

For two lines to be parallel, they must have the same slope. Let's check the slopes of the given options:

**Option #1:** \( y = 14x + 8 \)
- Slope is \( 14 \). (This line is parallel.)

**Option #2:** \( 4y = x + 8 \)
- Rearranging this gives:
\( y = \frac{1}{4}x + 2 \)
- Slope is \( \frac{1}{4} \). (Not parallel.)

**Option #3:** \( y = 4x + 2 \)
- Slope is \( 4 \). (Not parallel.)

**Option #4:** \( y = -4x + 8 \)
- Slope is \( -4 \). (Not parallel.)

The line in **Option #1** \( y = 14x + 8 \) is parallel to the given line.

So, the answer is:

**The line in Option #1 is parallel to the given line.**