Parallel lines must have identical slopes. The given equation is in the $\displaystyle y=mx+b$ form. Therefore, we can quickly determine that its slope is 3. The only other equation with a slope of 3 is $\displaystyle y=3x-4$.

Parallel lines have the same slope. Since all of these equations are in the $\displaystyle y=mx+b$ form, it is easy to determine their slopes, $\displaystyle m$. The slope of $\displaystyle y=2x-3$ is 2.

The only other line with a slope of 2 is $\displaystyle y=2x+5$.

Parallel lines must have equal slopes to one another. Since all of the lines are in the $\displaystyle y=mx+b$ form, it is easy to determine their slopes. The given line has a slope of 3, which means that any line that is parallel to it must have a slope of 3. The only other line with a slope of 3 is $\displaystyle y=3x+6$.

Parallel lines have the same slope as one another. The only pair of lines with the same slope is $\displaystyle y=6x+5; y=6x-3$.

Parallel lines have identical slopes with one another. The given line has a slope of 9, so its parallel line must also have a slope of 9. The only other line with a slope of 9 is $\displaystyle y=9x-4$.

Parallel lines have identical slopes. Since all of these lines are in the $\displaystyle y=mx+b$ form, you can easily determine their slopes ($\displaystyle m$). The slope of the given line is $\displaystyle \frac{5}{4}$, so a line that's parallel to it must have the same slope. The only other line with a slope of $\displaystyle \frac{5}{4}$ is $\displaystyle y=\frac{5}{4}x-9$.

Parallel lines have identical slopes, so you must figure out which of these lines have the same slope as the given line. To determine the slope of the given line, you can rearrange it to resemble the $\displaystyle y=mx+b$ form. $\displaystyle 2y-3x=10$ can be rearranged to $\displaystyle y=\frac{3}{2}x+5$. Looking at the rearranged equation, it is clear that the line's slope is $\displaystyle \frac{3}{2}$. The only other line with a slope of $\displaystyle \frac{3}{2}$ is $\displaystyle y=\frac{3}{2}x+8$.

Parallel lines have identical slopes to one another. The slope of the given line is 7, so the slope of the other line must also be 7. The only other equation with a slope of 7 is $\displaystyle y=7x-4$.

The first equation is written in standard form: $\displaystyle \small Ax+By=C$. In this format, the slope is equal to $\displaystyle -\frac{A}{B}$.

$\displaystyle \small 3x+2y=12$

$\displaystyle \small A=3\ \text{and}\ B=2$

$\displaystyle \small m=-\frac{A}{B}=-\frac{3}{2}$

The second equation is written in slope-intercept form: $\displaystyle \small y=mx+b$. The slope is given by the value of $\displaystyle \small m$.

$\displaystyle \small y=-\frac{3}{2}x+7$

$\displaystyle \small m=-\frac{3}{2}$

Because the slopes of both lines are equal, the lines must be parallel.

Parallel lines have the same slope. To find the slope of a given equation, it is necessary to convert it to slope-intercept form.

$\displaystyle 2x - 4y = 7$

Subtract the $\displaystyle \small 2x$ from both sides.

$\displaystyle -4y=-2x+7$

Divide by $\displaystyle \small -4$.

$\displaystyle y=\frac{1}{2}x-\frac{7}{4}$

Understanding slope-intercepts form, we can see that the slope is $\displaystyle \small m=\frac{1}{2}$.

We can convert each answer choice to slope-intercept form to detrmine which has a slope matching the equation in the question.

$\displaystyle 7x - 14y = 32\rightarrow y=\frac{1}{2}x-\frac{32}{14}$

This equation has the same slope, and is therefore parallel.