Question

Are the Lines Parallel, Perpendicular, or Intersecting?

y=13x+2

2y+6x=4

(1 point)
Responses

Intersecting
Intersecting

Parallel
Parallel

Perpendicular

Answer 1

To determine the relationship between the two lines given by the equations, we need to analyze their slopes.

**The first equation:**
\[ y = 13x + 2 \]
This is in slope-intercept form (y = mx + b), where the slope \( m \) is 13.

**The second equation:**
\[ 2y + 6x = 4 \]
First, we'll rewrite this in slope-intercept form.

1. Subtract \( 6x \) from both sides:
\[ 2y = -6x + 4 \]

2. Divide each term by 2:
\[ y = -3x + 2 \]
This gives us a slope of \( m = -3 \).

Now we can compare the slopes:
- The slope of the first line is 13.
- The slope of the second line is -3.

**Analyzing the slopes:**
- Since the slopes (13 and -3) are not equal, the lines are not parallel.
- Additionally, the product of their slopes is:
\[ 13 \times (-3) = -39 \]
Since the product is not equal to -1, the lines are not perpendicular.

**Conclusion:**
Since the lines are neither parallel nor perpendicular, they must be intersecting.

Therefore, the correct response is **Intersecting**.