Question

True or False: 2y = -3x + 8 is an equation that represents a line parallel to the line 6x + 2y = 9.

Answer 1

For this case we have by definition, that if two lines are parallel then their slopes are equal.

We manipulate the equations algebraically to take them to the form y = mx + b.

Equation 1:

$2y = -3x + 8\\y = - \frac {3} {2} x + 4$

Thus, the slope of this line is $- \frac {3} {2}.$

Equation 2:

$6x + 2y = 9\\2y = 9-6x\\2y = -6x + 9\\y = \frac {-6x + 9} {2}\\y = -3x + \frac {9} {2}$

The slope of this line is -3.

As the slopes are not equal, then the lines are not parallel.

Answer:

False