Lines can be written in the slope-intercept format:

\(\displaystyle y=mx+b\)

In this format, \(\displaystyle m\) equals the line's slope and \(\displaystyle b\) represents where the line intercepts the y-axis.

In the given equation:

\(\displaystyle m=\frac{1}{2}\)

Parallel lines share the same slope.

Only one of the choices has a slope of \(\displaystyle \frac{1}{2}\).

\(\displaystyle y=\frac{1}{2}x+\frac{17}{2}\)

Lines can be written in the slope-intercept format:

\(\displaystyle y=mx+b\)

In this format, \(\displaystyle m\) equals the line's slope and \(\displaystyle b\) represents where the line intercepts the y-axis.

In the given equation:

\(\displaystyle m=6\)

Parallel lines share the same slope.

Only one of the choices has a slope of \(\displaystyle 6\).

\(\displaystyle y=6x-14\)

By definition, lines are parallel if they have the same slope. Given that the reference equation provided is in the \(\displaystyle y=mx+b\) form, we can quickly deduce that the slope is \(\displaystyle \small 2\) \(\displaystyle \small (m=2)\). Out of the provided options there is only one answer that offers a slope of \(\displaystyle 2\), therefore that is the correct answer. The y-intercept is not a determinant of lines being parallel or perpendicular. 

Parrallel lines, by definition have the same slope, or \(\displaystyle m\). 

You must get the second equation into \(\displaystyle y=mx+b\) form. To do this you need to multiply everything by \(\displaystyle 3\), the reciprocate of one-third. So:

\(\displaystyle 3(\frac{1}{3}y=x+50)\) 

Which simplifies to  \(\displaystyle y=3x+150\)

because the first and second equation have the same slope, they are parrallel.

Two lines are parellel if they have the same slope.  If we look at an equation of a line in slope-intercept form

\(\displaystyle y = mx + b\)

we know that m equals the slope.  So, in the equation

\(\displaystyle y = 4x - 12\)

the slope of the line is 4.  So, the answer must also have a slope of 4.  If we look at 

\(\displaystyle 4y = 16x +24\)

we must write it in slope-intercept form.  To do that, we must get y by itself.  We must divide each term by 4.  We get

\(\displaystyle \frac{4y}{4} = \frac{16x}{4} + \frac{24}{4}\)

\(\displaystyle y = 4x + 6\)

The slope of this line is 4.  Therefore, it is parallel to the original line.

Which of the following lines is parallel to h(t)?

\(\displaystyle h(t)=14t+156\)

Parallel lines have equal slope. In h(t), our slope is 14, so we need the other choice with a slope of 14.

Only one other option has a slope of 14, and that is:

\(\displaystyle y=14t-989\)

Don't be fooled by lines with the same y-intercept. Slope is all that matters here!

Parallel lines have the same slope. If they didn't, the lines would eventually intersect and certainly would not be parallel. The slope is m in y=mx+b form. Since all of these lines are in slope intercept form just select the two that have the same slope.

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

\(\displaystyle y=\frac{1}{2}x+5\)

When comparing two lines to see if they are parallel, they must 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.  

The original equation

\(\displaystyle 4y = -2x + 8\)

will need to be written in slope-intercept form.  To do that, we will divide each term by 4

\(\displaystyle \frac{4y}{4} = \frac{-2x}{4} + \frac{8}{4}\)

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

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

Therefore, the slope of the original line is \(\displaystyle -\frac{1}{2}\).  A line that is parallel to this line will also have a slope of \(\displaystyle -\frac{1}{2}\).

Therefore, the line

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

is parallel to the original line.

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

\(\displaystyle 5y = -15x + 20\)

we must solve for y.  To do that, we will divide each term by 5.  We get

\(\displaystyle \frac{5y}{5} = \frac{-15x}{5} + \frac{20}{5}\)

\(\displaystyle y = -3x + 4\)

We can see the slope of this line is -3.  Therefore, this line is parallel to the line 

\(\displaystyle y = -3x + 1\)

because it also has a slope of -3.

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:

\(\displaystyle y=4x+2\)

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

The first line has a slope of 4, while the second has a slope of 2 meaning the lines are not parallel.