The equation is written in slope-intercept form, which is:
\(\displaystyle \small y=mx+b\)

where \(\displaystyle m\) is equal to the slope and \(\displaystyle b\) is equal to the y-intercept. Therefore, a line depicted by the equation

\(\displaystyle \small y=-\frac{1}{3}x+7\)

has a slope that is equal to \(\displaystyle -\frac{1}{3}\) and a y-intercept that is equal to \(\displaystyle 7\).

The slope-intercept form of a line is: \(\displaystyle y=mx+b\), where \(\displaystyle m\) is the slope and \(\displaystyle b\) is the y-intercept.

In this equation, \(\displaystyle m \textup{ = }\frac{2}{3}\) and \(\displaystyle y \textup{ = }-8\)

The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is \(\displaystyle \frac{6}{40}\). Multiply this by 100% to get its equivalent percent:

\(\displaystyle \frac{6}{40} \times 100 \% = 15 \%\)

This is the correct choice.

Given two points, \(\displaystyle (x_{1}, y_{1}), (x_{2}, y_{2})\), the slope can be calculated using the following formula:

\(\displaystyle m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}\)

Set \(\displaystyle x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8\):

\(\displaystyle m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2\)

Convert the equation into slope-intercept form, which is \(\displaystyle y=mx+b\), where \(\displaystyle m\) is the slope and \(\displaystyle b\) is the y-intercept.

\(\displaystyle 3x+2y=-6\)

\(\displaystyle 3x-3x+2y=-6-3x\)

\(\displaystyle 2y=-6-3x\)

\(\displaystyle \frac{2y}{2}=\frac{-6-3x}{2}\)

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

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

\(\displaystyle b=-3\)

In order to find the perpendicular of a given slope, you need that given slope!  This is easy to compute, given your equation.  Just get it into slope-intercept form.  Recall that it is \(\displaystyle y=mx+b\)

Simplifying your equation, you get:

\(\displaystyle 6y=-3x+93\)

\(\displaystyle y=\frac{-1}{2}x+\frac{93}{6}\)

This means that your perpendicular slope (which is opposite and reciprocal) will be \(\displaystyle 2\).

First, you should solve for the slope of the line passing through your two points.  Recall that the equation for finding the slope between two points is:

\(\displaystyle \frac{rise}{run} = \frac{y_2-y_1}{x_2-x1}\)

For your data, this is

\(\displaystyle \frac{19-4}{7-2}=\frac{15}{5}=3\)

Now, recall that perpendicular slopes are opposite and reciprocal.  Therefore, the slope of your line will be \(\displaystyle \frac{-1}{3}\).   Given that all of your options are in slope-intercept form, this is somewhat easy.  Remember that slope-intercept form is:

\(\displaystyle y=mx+b\)

\(\displaystyle m\) is your slope.  Therefore, you are looking for an equation with \(\displaystyle m=\frac{-1}{3}\)

The only option that matches this is:

\(\displaystyle y=\frac{-1}{3}x+94\)

Remember, to find the x-intercept, you need to set \(\displaystyle y\) equal to zero.  Therefore, you get:

\(\displaystyle 3x=159\)

Simply solving, this is \(\displaystyle x=53\)

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result, \(\displaystyle -3y=-2x+4\)

Step 2: Recall the basic equation of a line...

\(\displaystyle y=mx+b\), where the coefficient of y is \(\displaystyle 1\).

Step 3: Divide every term by \(\displaystyle -3\) to change the coefficient of y to \(\displaystyle 1\):

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

Step 4: Reduce...

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

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is \(\displaystyle \frac {2}{3}\)

In order to find the slope, we will need the equation in slope-intercept form.

 \(\displaystyle y=mx+b\)

Distribute the negative nine through the binomial.

\(\displaystyle y=(-9)(-x)+(-9)(6) = 9x-54\)

The slope is:  \(\displaystyle 9\)