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.

First, put the given line in \(\displaystyle y=mx+b\) form.

\(\displaystyle 20y-16x=40\)

We need to isolate \(\displaystyle y\) on the left side of the equation. Add \(\displaystyle 16x\) to both sides of the equation.

\(\displaystyle 20y-16x+16x=40+16x\)

Simplify.

\(\displaystyle 20y=40+16x\)

Divide both sides of the equation by \(\displaystyle 20\).

\(\displaystyle \frac{20y}{20}=\frac{40}{20}+\frac{16x}{20}\)

Simplify.

\(\displaystyle y=2+\frac{16}{20}x\)

Reduce.

\(\displaystyle y=2+\frac{4}{5}x\)

Rearrange terms to match the slope-intercept form.

\(\displaystyle y=\frac{4}{5}x+2\)

In the given equation:

\(\displaystyle m=\frac{4}{5}\)

Parallel lines share the same slope.

Only one of the choices has a slope of \(\displaystyle \frac{4}{5}\).

\(\displaystyle y=\frac{4}{5}x+\frac{1}{2}\)

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.

First, put the given line in \(\displaystyle y=mx+b\) form.

\(\displaystyle 7y-14x=16\)

We need to isolate \(\displaystyle y\) on the left side of the equation. Add \(\displaystyle 14x\) to both sides of the equation.

\(\displaystyle 7y-14x+14x=16+14x\)

Simplify.

\(\displaystyle 7y=16+14x\)

Divide both sides of the equation by \(\displaystyle 7\).

\(\displaystyle \frac{7y}{7}=\frac{16}{7}+\frac{14x}{7}\)

Simplify.

\(\displaystyle y=\frac{16}{7}+2x\)

Rearrange terms to match the slope-intercept form.

\(\displaystyle y=2x+\frac{16}{7}\)

In the given equation:

\(\displaystyle m=2\)

Parallel lines share the same slope.

Only one of the choices has a slope of \(\displaystyle 2\).

\(\displaystyle y=2x-\frac{4}{7}\) 

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.

First, put the given line in \(\displaystyle y=mx+b\) form.

\(\displaystyle 12y-18x=24\)

We need to isolate \(\displaystyle y\) on the left side of the equation. Add \(\displaystyle 18x\) to both sides of the equation.

\(\displaystyle 12y-18x+18x=24+18x\)

Simplify.

\(\displaystyle 12y=24+18x\)

Divide both sides of the equation by \(\displaystyle 12\).

\(\displaystyle \frac{12y}{12}=\frac{24}{12}+\frac{18x}{12}\)

Simplify.

\(\displaystyle y=2+\frac{18}{12}x\)

Reduce.

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

Rearrange terms to match the slope-intercept form.

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

n the given equation:

\(\displaystyle m=\frac{3}{2}\)

Parallel lines share the same slope.

Only one of the choices has a slope of \(\displaystyle \frac{3}{2}\).

\(\displaystyle y=\frac{3}{2}x-8\)

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.

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

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