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,

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

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,

\(\displaystyle \text{Slope}=\frac{-4-9}{1-5}=\frac{-13}{-4}=\frac{13}{4}\)