Which best describes the relationship between the lines with equations -5x-8y=4 and -30-48y=24

Answer 1

Notice that with the first equation, -5x - 8y = 4,

6·( -5x - 8y) = 6·4 <---> -30x -48y = 24

This is the second equation. What this means is -5x - 8y = 4 and -30x -48y = 24 describe the same line.

Answer 2

Should the second equation be: -30x - 48y = 24?

If so, these equations are for parallel lines.

You can see this if you recognize that each of the terms in the first equation (-5x, -8y, 4) is multiplied by 6 to get the terms in the 2nd equation: -30x, -48y, 24

Even better, if you write each equation in slope-intercept form (y = mx + b), you'll see that the slope in each equation (the "m" in y = mx + b) is the same.

Re-write the 1st equation: y = -5/8x -4/8

Re-write the 2nd equation: y = -30/48x - 24/48

The slope in each is -5/8 (-30/48 simplifies to -5/8)

Definition: Two lines with the same slope are parallel