Question

A student wrote the following equations 3y+6=2x && 2y-8x=6 the lines represented by these equations are ... A) parallel b ) the same line c) perpendicular or D) intersecting but not perpendicular

Answer 1

i really need help guys

Answer 2

\[A student wrote the following equations 3y+6=2x && 2y-8x=6 the lines represented by these equations are ... A) \parallel b ) the same line c) perpendicular or D) intersecting but \not perpendicular\]

Answer 3

First turn them into slope intercept form by isolating the y...
3y + 6 = 2x
3y = 2x - 6
y = 2/3x -2

2y - 8x = 6
2y = 8x + 6
y = 4x + 3

What can you tell from comparing the equations in slope intercept form?

Answer 4

Clearly they're not the same line. Since the slopes aren't the same, the lines aren't parallel and since the slopes aren't opposite reciprocals, they aren't parallel, either. That leaves D, the lines are intersecting but not perpendicular.