Question

Which best describes the relationship between the lines?

2x – y = −1


4x – 2y = 6


same line


perpendicular


neither


parallel

Answer 1

same line preparations

Answer 2

Parallel

Explanation:

So the best way to compare two lines is to convert it into slope-intercept form which is given in the form of: y=mx+b where m is the slope, and b is the y-intercept, in this form it's really easy to see if they're the same line, parallel, or perpendicular.

Original Equation:

2x - y = -1

Subtract 2x from both sides

-y = -2x - 1

Divide both sides by -1

y = 2x + 1

Original Equation:

4x - 2y = 6

Subtract 4x from both sides

-2y = -4x + 6

Divide both sides by -2

y = 2x - 3

As you can see both equations have a slope of 2, but different y-intercepts, so they're not the same line, but they'll also never intersect, because they increase by the same amount, thus they are parallel