The coordinates of the plotted points are $(1,0)$ and $(3,6).$ So, we let $(x_1,y_1) = (1,0)$ and $(x_2,y_2) = (3,6),$ and compute the slope using the formula:

\[ \eqalign{ m &= \dfrac {y_2 - y_1} {x_2 - x_1} \\[5pt] &= \dfrac {6 - 0} {3 - 1} \\[5pt] &= \dfrac {6} {2} \\[5pt] &= 3 } \]

Thus, the slope is $m=3.$

We let $(x_1,y_1) = (4,5)$ and $(x_2,y_2) = (2,3),$ and compute the slope using the formula:

\begin{eqnarray} \eqalign{ m &= \dfrac {y_2 - y_1} {x_2 - x_1} \\[5pt] &= \dfrac {3-5} {2-4} \\[5pt] &= \dfrac {-2} {-2} \\[5pt] &= 1 } \end{eqnarray}

Thus, the slope is $m=1.$

Note that the line passes through the points $(0,4)$ and $(2,0).$ So, we let $(x_1,y_1) = (0,4)$ and $(x_2,y_2) = (2,0),$ and compute the slope using the formula:

\begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &= \dfrac{0-(4)}{2-0} \\[5pt] &= \dfrac{-4}{2} \\[5pt] &= -2 \end{align*}

Therefore, the slope of the line is $m=-2.$

Note that the line passes through the points $(-4,0)$ and $(0,2).$ So, we let $(x_1,y_1) = (-4,0)$ and $(x_2,y_2) = (0,2),$ and compute the slope using the formula:

\begin{align*} m &= \dfrac{y_2-y_1}{x_2-x_1} \\[5pt] &= \dfrac{2-0}{0-(-4)} \\[5pt] &= \dfrac{2}{4} \\[5pt] &= \dfrac{1}{2} \end{align*}

Therefore, the slope of the line is $m=\dfrac{1}{2}.$

The slope of the vertical line is undefined. We can see this by choosing two points on the line, such as $(0.5,0)$ and $(0.5,1),$ and computing the slope between them:

\begin{align*} m = \dfrac{y_2 - y_1}{x_2-x_1} = \dfrac{1-0}{0.5-0.5} = \dfrac{1}{0} = \text{undefined} \end{align*}

The line is horizontal, and therefore it has a slope of zero.

We can also see this by choosing two points on the line, such as $(0,-1.5)$ and $(1,-1.5),$ and computing the slope between them:

\begin{align*} m = \dfrac{y_2 - y_1}{x_2-x_1} = \dfrac{(-1.5)-(-1.5)}{1-0} = \dfrac{-1.5+1.5}{1} = \dfrac 0 1 = 0 \end{align*}

Remember that slope is the amount the line rises vertically per unit that it runs horizontally.

Since the graph decreases ($\searrow$) as we go from left to right, the line rises by a negative amount.

Therefore, the slope of the line is negative.

Remember that slope is the amount the line rises vertically per unit that it runs horizontally.

Since the graph increases ($\nearrow$) as we go from left to right, the line rises by a positive amount.

Therefore, the slope of the line is positive.