what equation represents a line parallel to the line whose equation is 2y − 5x = 10?

Question

1.   5y + 2x = 10
2.   2y + 10x = 8
3.   5y − 2x = 25
4.   4y − 10x = 12

which one?

 

Answer 1

We know that parallel lines have equal slope.

Given line equation 2y-5x = 10

Add 5x to each side.

2y-5x+5x = 10+5x

2y = 5x+10

Divide to each side by 2.

y = (5/2)x+5

Compare it slope intercept form of line y = mx+b

m = 5/2.

1) 5y+2x = 10

5y = -2x+10

y = (-2/5)x+2

m = -2/5

2) 2y+10x = 8

2y = -10x+8

y = -5x+4

m = -5

3) 5y-2x = 25

5y = 2x+25

y = (2/5)x+5

m = 2/5

4) 4y-10x = 12

4y = 10x+12

y = (5/2)x+3

m = 5/2

Given line 2y-5x = 10 and 4y-10x = 12 have equal slopes.

The correct choice is 4.

Comments

Since parallel lines have same slopes.

The line 2y - 5x = 10 is parallel to 4y-10x = 12.

Option 4 is the correct choice.