Parallel lines have the same slope. The slope of a line in slope-intercept form \(\displaystyle (y=mx+b)\) is the value of \(\displaystyle m\). So, the slope of the line \(\displaystyle y=-3x+1\) is \(\displaystyle -3\). That means that for the two lines to be parallel, the slope of the second line must also be \(\displaystyle -3\).

Parallel lines have the same slope. The slope of a line in slope-intercept form \(\displaystyle (y=mx+b)\) is the value of \(\displaystyle m\). So, the slope of the line \(\displaystyle y=\frac{1}{4}x+3\) is \(\displaystyle \frac{1}{4}\). That means that for the two lines to be parallel, the slope of the second line must also be \(\displaystyle \frac{1}{4}\).

Parallel lines have the same slope. The slope of a line in slope-intercept form \(\displaystyle (y=mx+b)\) is the value of \(\displaystyle m\). So, the slope of the line \(\displaystyle y=9x-2?\) is \(\displaystyle 9\). That means that for the two lines to be parallel, the slope of the second line must also be \(\displaystyle 9\).

Parallel lines have the same slope. Start by putting the given equation in \(\displaystyle y=mx+b\) form to figure out its slope:

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

Subtract \(\displaystyle 4x\) from each side of the equation:

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

Divide each side of the equation by \(\displaystyle -2\):

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

The slope of both this line and the one parallel to it must be \(\displaystyle 2\).

Parallel lines have the same slope. Start by putting the given equation in \(\displaystyle y=mx+b\) form to figure out its slope.

\(\displaystyle 10x-2y=12\)

Divide both sides of the equation by \(\displaystyle 2\):

\(\displaystyle 5x-y=6\)

Subtract \(\displaystyle 5x\) from both sides of the equation:

\(\displaystyle -y=-5x+6\)

Divide both sides of the equation by \(\displaystyle -1\):

\(\displaystyle y=5x-6\)

The given line has a slope of \(\displaystyle 5\), so the answer choice equation needs to have a slope of \(\displaystyle 5\) as well.

Parallel lines have the same slope. Start by putting the given equation in \(\displaystyle y=mx+b\) form to figure out its slope.

\(\displaystyle 3x+4y=9\)

Subtract \(\displaystyle 3x\) from each side of the equation:

\(\displaystyle 4y=-3x+9\)

Divide both sides of the equation by \(\displaystyle 4\):

\(\displaystyle y=-\frac{3}{4}x+\frac{9}{4}\)

The given line has a slope of \(\displaystyle -\frac{3}{4}\), so the answer choice equation will need to have a slope of \(\displaystyle -\frac{3}{4}\) as well to be parallel to the given line.

Parallel lines have the same slope. Start by putting the given equation in \(\displaystyle y=mx+b\) form to figure out its slope.

\(\displaystyle 9x+6y=12\)

Subtract \(\displaystyle 9x\) from each side of the equation:

\(\displaystyle 6y=-9x+12\)

Divide each side of the equation by \(\displaystyle 6\) and reduce:

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

The given line has a slope of \(\displaystyle -\frac{3}{2}\), so the answer choice equation will need to have a slope of \(\displaystyle -\frac{3}{2}\) as well to be parallel to the given line.

Parallel lines have the same slope. Start by putting the given equation in \(\displaystyle y=mx+b\) form to figure out its slope.

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

Subtract \(\displaystyle 2x\) from each side of the equation:

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

Divide each side of the equation by \(\displaystyle -1\):

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

Since the presented equation has a slope of \(\displaystyle 2\), the correct answer choice's equation will also have a slope of \(\displaystyle 2\). This makes the correct answer \(\displaystyle y=2x-1\).

Parallel lines have the same slope. First, put the given equation in \(\displaystyle y=mx+b\) form to find its slope.

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

Subtract \(\displaystyle 7x\) from both sides of the equation:

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

The given line has a slope of \(\displaystyle -7\), so the correct answer will also have a slope of \(\displaystyle -7\). This means that the correct answer choice is \(\displaystyle y=-7x-2\).

For two lines to be parallel, their slopes must be the same. Since the slope of the given line is \(\displaystyle \frac{2}{3}\), the line that is parallel to it must also have a slope of \(\displaystyle \frac{2}{3}\).