For what value of a are the lines of 6y=-2x+4 and 2y=ax-5 parallel? perpendicular?

Hey there!!

Parallel lines have the same slope. If they have different slope, then they are not parallel because both lines would combine at some point.

The y-intercept form:

y = mx + b

In this equation, 'm' is considered to be the slope.

The equation we have is 6y = -2x + 4

First, let's divide all the sides with 6 to isolate the value of 'y'.

... 6y = -2x + 4

... y = -1/3x + 2/3

The slope is -1/3...

... hence the slope in the other equation should be -1/3.

Equation we got...

... 2y = ax - 5

Let's divide by 2 on both sides...

... y = ax/2 - 5

The slope in this a/2

Hence, ...

... a/2 = -1/3

... 3a = -2

... a = -2/3