In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

\(\displaystyle y=mx+b\)

Do that for each line:

\(\displaystyle 4y-2=x\rightarrow 4y=x+2\rightarrow y=\frac{1}{4}x+\frac{1}{2}\)

\(\displaystyle 6y-3=2x\rightarrow 6y=2x+3\rightarrow y=\frac{1}{3}x+\frac{1}{2}\)

The first line has a slope of 1/4, while the second has a slope of 1/3 meaning the lines are not parallel.

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

\(\displaystyle y=mx+b\)

Do that for each line:

\(\displaystyle x-y=4\rightarrow -y=-x+4\rightarrow y=x-4\)

\(\displaystyle 2x-3y=4\rightarrow -3y=-2x+4\rightarrow y=\frac{2}{3}x-\frac{4}{3}\)

The first line has a slope of 1, while the second has a slope of 2/3 meaning the lines are not parallel.

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

\(\displaystyle y=mx+b\)

Do that for each line:

\(\displaystyle 6x+y=12\rightarrow y=-6x+12\)

\(\displaystyle 5x+2y=15\rightarrow 2y=-5x+15\rightarrow y=\frac{-5}{2}x+3\)

The first line has a slope of -6, while the second has a slope of -5/2 meaning the lines are not parallel.

In order to determine if two lines have the same slope first write them according to slope-intercept form, where "m" is the slope of the line:

\(\displaystyle y=mx+b\)

Do that for each line:

\(\displaystyle y-3x=12\rightarrow y=3x+12\)

\(\displaystyle y+2x=6\rightarrow y=-2x+6\)

The first line has a slope of 3, while the second has a slope of -2 meaning the lines are not parallel.

Two lines are parallel when they have the same slope.  We can compare slopes when we write the equation of the line in slope-intercept form

\(\displaystyle y = mx+b\)

where m is the slope.  Given the original equation

\(\displaystyle 6y = -42x + 36\)

we must write it in slope-intercept form to find the slope.  To do this, we will divide each term by 6.  We get

\(\displaystyle \frac{6y}{6} = \frac{-42x}{6} + \frac{36}{6}\)

\(\displaystyle y = -7x + 6\)

Therefore, the slope of the original line is -7.  A line that is parallel to this line needs to have a slope of -7.

Let's look at the equation of the line 

\(\displaystyle -8y = 56x + 64\)

We must write it in slope-intercept form.  To do this, we will divide each term by -8.  We get

\(\displaystyle \frac{-8y}{-8} = \frac{56x}{-8} + \frac{64}{-8}\)

\(\displaystyle y = -7x - 8\)

The slope of this line is -7.  Therefore, it is parallel to the original line.

For the lines to be parallel, both the lines must have similar slopes.

Write the slope-intercept form.

\(\displaystyle y=mx+b\)

The \(\displaystyle m\) represents the slope.  Both of the equation have a slope of negative three.  Therefore, both lines are parallel.

The answer is:  \(\displaystyle \textup{Yes, the lines are parallel since slopes are alike.}\)

If two lines are parallel, then they have the same slope.  To find the slope of a line, we write it in slope-intercept form

\(\displaystyle y = mx+b\)

where m is the slope.  So given the equation

\(\displaystyle 6y = -42x + 18\)

we must solve for y.  To do that, we will divide each term by 6.  We get

\(\displaystyle \frac{6y}{6} = \frac{-42x}{6} + \frac{18}{6}\)

\(\displaystyle y = -7x + 3\)

We can see the slope of this line is -7.  Therefore, this line is parallel to the line 

\(\displaystyle y = -7x + 1\)

because it also has a slope of -7.

When looking at parallel lines, the slopes on both lines must be the same.  The y-intercept (or any other characteristic) of the lines do not matter. 

As long as the slopes are the same, the lines are parallel.

In order to determine whether if the lines are parallel, the lines must never intersect and share a similar slope to the equation given in the problem.

The equation is already in the form of:  \(\displaystyle y=mx+b\)

The variable \(\displaystyle m\) denotes the slope of the function.

The slope of the other line must be three to be parallel.  

The only possible answer is:  \(\displaystyle y=3x+5\)

\(\displaystyle y=mx+b\)

the lines are parallel if both of the following conditions are met

• \(\displaystyle m\) is the same value for both equations
• \(\displaystyle b\) are different values in the two equations

For the lines

\(\displaystyle y=2x+7\)

\(\displaystyle y=3x-5\)

we see that the \(\displaystyle m\) values are not the same and as such

the lines are NOT parallel.