Question

Select the answer that represents parallel lines



a
4x=10y+6

y=-(5/2)x+3

b
y=4x-6

4y=24x-8

c
5y=10x+20

-8x=-4y+4

Answer 1

To determine which pair of equations represents parallel lines, we need to recognize that parallel lines have the same slope.

Let's rewrite each pair of equations in slope-intercept form (y = mx + b), where m is the slope.

**Option a:**
1. \( 4x = 10y + 6 \)
- Rearranging: \( 10y = 4x - 6 \)
- Dividing by 10: \( y = \frac{2}{5}x - \frac{3}{5} \) (slope = \( \frac{2}{5} \))

2. \( y = -\frac{5}{2}x + 3 \) (slope = \( -\frac{5}{2} \))

These lines have different slopes, so they are not parallel.

**Option b:**
1. \( y = 4x - 6 \) (slope = \( 4 \))

2. Rearranging \( 4y = 24x - 8 \):
- Dividing by 4: \( y = 6x - 2 \) (slope = \( 6 \))

These lines have different slopes, so they are not parallel.

**Option c:**
1. \( 5y = 10x + 20 \)
- Dividing by 5: \( y = 2x + 4 \) (slope = \( 2 \))

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

These lines have the same slope \(2\), so they are parallel.

Thus, the answer is **Option c**.