Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=\frac{2}{7}$

Only one of the choices has a slope of $\displaystyle \frac{2}{7}$:

$\displaystyle y=\frac{2}{7}x+12$

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=\frac{9}{4}$

Only one of the choices has a slope of $\displaystyle \frac{9}{4}$:

 $\displaystyle y=\frac{9}{4}x+3$ 

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=4$

Only one of the choices has a slope of $\displaystyle 4$:

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

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=-9$

Only one of the choices has a slope of $\displaystyle -9$:

$\displaystyle y=-9x+4$

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=-\frac{5}{6}$

Only one of the choices has a slope of $\displaystyle -\frac{5}{6}$:

$\displaystyle y=-\frac{5}{6}x-100$

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=-\frac{3}{8}$

Only one of the choices has a slope of $\displaystyle -\frac{3}{8}$:

$\displaystyle y=-\frac{3}{8}x-1$

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=-\frac{1}{10}$

Only one of the choices has a slope of $\displaystyle -\frac{1}{10}$:

$\displaystyle y=-\frac{1}{10}x+55$

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=\frac{8}{7}$

Only one of the choices has a slope of $\displaystyle \frac{8}{7}$:

$\displaystyle y=\frac{8}{7}x-\frac{2}{3}$ 

Lines that are parallel have the same slope. Lines can be written in the slope-intercept form:

$\displaystyle y=mx+b$

In this equation, $\displaystyle m$ equals the slope and $\displaystyle b$ represents the y-intercept.

In the given equation:

 $\displaystyle m=-14$

Only one of the choices has a slope of $\displaystyle -14$:

$\displaystyle y=-14x+23$

Lines can be written using the slope-intercept equation format:

$\displaystyle y=mx+b$

Lines that are parallel have the same slope.

The given line has a slope of:

$\displaystyle m=20$

Only one of the choices also has the same slope and is the correct answer:

$\displaystyle y=20x+12$