To answer this question, we must find the slope of a line parallel to the line \(\displaystyle 8x+2y=3\).

When a line is parallel to another, they have the same slope. Therefore, if we find the slope of the line we are given, we will find the slope of any line that would be parallel to it. 

To find the slope, we must put our equation into point-intercept form. Point-intercept form is displayed as the following:

\(\displaystyle y=mx+b\), where \(\displaystyle m\) is the slope and \(\displaystyle b\) is where the line intercepts the \(\displaystyle y\)-axis.

Note that to put a line into point-intercept form, you must solve for \(\displaystyle y\).

Therefore, we must solve for \(\displaystyle y\). So, for this data, we must first subtract both sides of the equation by \(\displaystyle 8x\):

\(\displaystyle 8x+2y=3\rightarrow 8x+2y-8x=3-8x\)

This becomes:

\(\displaystyle 2y=-8x+3\)

Now we must divide each side by \(\displaystyle 2\) to get \(\displaystyle y\) by itself:

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

This becomes:

\(\displaystyle y=-4x+\frac{3}2{}\)

Because \(\displaystyle -4\) is \(\displaystyle m\) in our point-intercept form, the slope of our line is \(\displaystyle -4\). Therefore, the slope of any line parallel to this line is also \(\displaystyle -4\).

Parallel lines have the same slope. You find slope by using the general form of slope-intercept:

\(\displaystyle y = mx+b\)

where \(\displaystyle m\) represents the slope of the line and \(\displaystyle b\) represents the \(\displaystyle y\)-intercept.

For our equation we see that the 

\(\displaystyle y = -4x + 1\)

\(\displaystyle m\) is \(\displaystyle -4\)

thus the anser is \(\displaystyle m = -4\).

The slope of a line in slope-intercept form is given by the coefficient, \(\displaystyle m\) in the equation:

\(\displaystyle y = mx + b\). For two lines to be parallel, they have to have the same slope. Thus we see in our equation that \(\displaystyle m = -8\) and so a line that is parallel must also have a slope of \(\displaystyle -8\)

Parallel lines have equivalent slopes, so the correct answer is \(\displaystyle y=2x+4\).

First write the equation in slope intercept form. Add \(\displaystyle 12x\) to both sides to get \(\displaystyle 4y = 12x + 2\). Now divide both sides by \(\displaystyle 4\) to get \(\displaystyle y = 3x + 0.5\). The slope of this line is \(\displaystyle 3\), so any line that also has a slope of \(\displaystyle 3\) would be parallel to it. The correct answer is  \(\displaystyle x - \frac{1}{3}y = 7\).

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "\(\displaystyle m\)" spot in the linear equation \(\displaystyle (y=mx+b)\), 

We are looking for an answer choice in which both equations have the same \(\displaystyle m\) value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

\(\displaystyle -4y=-10+26\)

\(\displaystyle y=\frac{10}{4}x-\frac{26}{4}\)

\(\displaystyle y=\frac{5}{2}x-\frac{13}{2}\)

Because the given line has the slope of \(\displaystyle \frac{5}{2}\), the line parallel to it must also have the same slope.

Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line \(\displaystyle P\) contains points \(\displaystyle (4, 2)\) and \(\displaystyle (-2, -2)\), so we can apply our slope formula directly (pay attention to negative signs!)

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1} = \frac{2+2}{4+2} = \frac{4}{6} = \frac{2}{3}\).

Line \(\displaystyle Q\) contains point \(\displaystyle (2,3)\) and, since the y-intercept is always on the vertical axis, \(\displaystyle (0,0)\). Thus:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1} = \frac{2-0}{3-0} = \frac{2}{3}\)

The two lines have the same slope, \(\displaystyle m=\frac{2}{3}\), and are thus identical.

We are told at the beginning of this problem that line \(\displaystyle A\) is described by  \(\displaystyle y=-3x+7\). Since \(\displaystyle y=mx+b\) is our slope-intecept form, we can see that \(\displaystyle m=-3\) for this line. Since parallel lines have equal slopes, we must determine if line \(\displaystyle B\) has a slope of \(\displaystyle -3\).

 Since we know that \(\displaystyle B\) passes through points \(\displaystyle (0,3)\) and \(\displaystyle (-3,0)\), we can apply our slope formula:

 \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1} = \frac{3-0}{0-(-3)} = \frac{3}{3} = 1\)

Thus, the slope of line \(\displaystyle B\) is 1. As the two lines do not have equal slopes, the lines are not parallel.