Write the formula for the slope.

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

Substitute the points.

\(\displaystyle m= \frac{9-(-1)}{-9-5} = \frac{10}{-14}\)

Reduce the fraction.

\(\displaystyle m= -\frac{5}{7}\)

The slope is \(\displaystyle -\frac{5}{7}\).

To find the slope of a line, we will write it in slope-intercept form

\(\displaystyle y = mx + b\)

where m is the slope.  Given the line

\(\displaystyle 18y = -72x + 36\)

we will need to solve for y, or get y to stand alone.  To do that, we will divide each term by 18.  So,

\(\displaystyle \frac{18y}{18} = \frac{-72x}{18} + \frac{36}{18}\)

\(\displaystyle y = -4x + 2\)

Using the information given above, we can see that the slope is -4.  

To find the slope of the line, we will need to re-format the equation back to slope-intercept form, \(\displaystyle y=mx+b\).

Add \(\displaystyle y\) on both sides.

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

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

Subtract \(\displaystyle 3x\) on both sides.

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

Simplify both sides.

\(\displaystyle y=6\)

This is a horizontal line and the value of \(\displaystyle m\) is zero.

The answer of the slope is:  \(\displaystyle 0\)

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

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

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

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

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

\(\displaystyle y = \frac{1}{2} x+ \frac{1}{3}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle \frac{1}{2}\), is the slope of the line.

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

\(\displaystyle 8y = 3x + 7\)

\(\displaystyle 8y \div 8 = (3x + 7) \div 8\)

\(\displaystyle y = \frac{3}{8}x+ \frac{7}{8}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle \frac{3}{8}\), is the slope of the line.

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

\(\displaystyle 7y+ 4x = 29\)

\(\displaystyle 7y+ 4x - 4x = 29 - 4x\)

\(\displaystyle 7y = -4x+ 29\)

\(\displaystyle 7y \div 7 = (-4x+ 29) \div 7\)

\(\displaystyle y = -\frac{4}{7}x + \frac{29}{7}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle -\frac{4}{7}\), is the slope of the line.

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

\(\displaystyle 9y - 4x = 30\)

\(\displaystyle 9y - 4x + 4x = 30+ 4x\)

\(\displaystyle 9y = 4x+ 30\)

\(\displaystyle 9y \div 9 = (4x+ 30) \div 9\)

\(\displaystyle y = \frac{4}{9} x + \frac{30}{9}\)

\(\displaystyle y = \frac{4}{9} x + \frac{10}{3}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle \frac{4}{9}\), is the slope.

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

\(\displaystyle x= 5y - 17\)

\(\displaystyle 5y - 17 = x\)

\(\displaystyle 5y - 17 + 17 = x + 17\)

\(\displaystyle 5y = x + 17\)

\(\displaystyle 5y \div 5 = (x + 17) \div 5\)

\(\displaystyle y= \frac{1}{5}x + \frac{17 }{5}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle \frac{1}{5}\), is the slope.

Rewrite the equation in slope-intercept form \(\displaystyle y = mx+b\):

\(\displaystyle 7x + 6y = 33\)

\(\displaystyle 7x + 6y - 7x = 33- 7x\)

\(\displaystyle 6y = -7x + 33\)

\(\displaystyle 6y \div 6 =( -7x + 33) \div 6\)

\(\displaystyle y = -\frac{7}{6}x + \frac{33}{6}\)

The coefficient of \(\displaystyle x\), which is \(\displaystyle -\frac{7}{6}\), is the slope.

In order to find the slope of this equation, we will need to put this in y-intercept form, \(\displaystyle y=mx+b\).

Simplify the equation by distribution and combine like-terms.

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

Simplify the parentheses.

\(\displaystyle y=4x-6+4x\)

Add like terms.

\(\displaystyle y=8x-6\)

The slope is \(\displaystyle 8\).