Question

Identify the equations as parallel lines, perpendicular lines, or neither.​

Answer 1

Parallel lines

Explanation:

Parallel lines have the same slope. Perpendicular lines have opposite (positive/negative) reciprocal slopes, and neither would be if the 2 slopes don't fit in either category.

If you set both the equations in standard form (y=), you get y = 2x-7 and y = 2x +5. The slopes of both is 2, so these are Pallarel lines.

Answer 2

Parallel

Explanation:

First put the equations in y = mx + b form

Equation 1 : -2x + y = -7

Add 2x to both sides

y = 2x - 7

Equation 2 : y - 5 = 2x

Add 5 to both sides

y = 2x + 5

Now that we have the equations in y = mx + b form we can determine whether the equations are parallel, perpendicular or neither

If the slopes are the same and the y intercepts are different then the equations are parallel

If the slopes are reciprocals then the equations are perpendicular.

If none of this happens then the answer is neither

The two equations y = 2x + 5 and y = 2x - 7 have a slope of 2 as well as different y intercepts therefore they are parallel