The slope is defined as the slant measurement of a line, quantitatively the amount of units that one must "rise", over the amout of units one must "run," or move horizontally across the graph. $\displaystyle \small \small (4,2)(14,6)$ are the points given.

We must find the slope of the line that would pass through both of these points.

To do so, we use the formula: 

$\displaystyle \small \frac{y_{1}-y_{2}}{x_{1}-x_{2}}{}$.

For these two points, our formula would look like this: 

$\displaystyle \small \small \frac{6-2}{14-4} = \frac{4}{10} = \frac{2}{5}$.

Thus $\displaystyle \small \small \frac{2}{5}$ is our slope. 

Rewrite the equation in slope intercept form.

$\displaystyle y=mx+b$

Where $\displaystyle m$ represents the slope of the line and $\displaystyle b$ represents the $\displaystyle y$-intercept.

$\displaystyle 10x+9y=8$

$\displaystyle 9y=-10x+8$

$\displaystyle y=-\frac{10}{9}x+8$

The slope is 

$\displaystyle -\frac{10}{9}$.

Use the given points and plug them into slope formula:

$\displaystyle m=\frac{\left ( y_{2}-y_{1} \right )}{(x_{2}-x_{1})}$

Remember points are written in the following format:

$\displaystyle (x,y)$

 Substitute.

$\displaystyle m=\frac{6-3}{4-2}$

Simplify:

$\displaystyle m=\frac{3}{2}$

The question asks for the slope of the line between two points.

*Always remember what the question is asking.

$\displaystyle Slope = m = rise/run = \frac{y_2-y_1}{x_2-x_1}$

Using coordinates

$\displaystyle (x_1, y_1)=({\color{Magenta} 0},{\color{DarkOrange} 4} ), (x_2,y_2)= ( 2,2)$,

and plugging them into the slope formula we get the following.

$\displaystyle \frac{2-{\color{DarkOrange} 4}}{2-{\color{Magenta} 0}} = \frac{-2}{2}= -1$

The question is asking for the slope of the equation.

$\displaystyle y=mx+b$ is the general form of an equation

"$\displaystyle m$" is the slope of the equation, meaning how steep the line of the representing graph would be.

In order to find $\displaystyle m$, you balance the equation to put it in the general format.

$\displaystyle \frac{y-3x}{2}=4$

$\displaystyle y-3x=8$

$\displaystyle y={\color{Magenta} 3}x+8$

$\displaystyle m={\color{Magenta} 3}$

To find the slope of a line, all we need is the coordinates of two points that lie on the line. We are provided with two points in this problem.

The formula used is: 

$\displaystyle \small \small \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

If we plug in the points provided: 

$\displaystyle \small \small \frac{7-4}{10-2}= \frac{3}{8}$.

Thus, our slope means that between these two points, we must rise 3 units and run 8 positive units. 

The slope of a line is given by the following equation:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

For the line in question,

$\displaystyle \text{Slope}=\frac{2-1}{6-(-5)}=\frac{1}{11}$

The slope of a line is given by the following equation:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

For the line in question,

$\displaystyle \text{Slope}=\frac{0-1}{6-(-1)}=-\frac{1}{7}$

The slope of a line is given by the following equation:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

For the line in question,

$\displaystyle \text{Slope}=\frac{-6-1}{-2-1}=\frac{-7}{-3}=\frac{7}{3}$

The slope of a line is given by the following equation:

$\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

For the line in question,

$\displaystyle \text{Slope}=\frac{0-5}{-1-10}=\frac{-5}{-11}=\frac{5}{11}$