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 \(\displaystyle 8\).

The given equation is currently in standard form.  In order to find the slope, we will need to isolate the \(\displaystyle y\) variable and put the equation in slope-intercept form.

The slope-intercept form is:  \(\displaystyle y=mx+b\)

Subtract \(\displaystyle \frac{1}{3}x\) from both sides.

\(\displaystyle \frac{1}{3}x+\frac{1}{4}y-\frac{1}{3}x=1-\frac{1}{3}x\)

Simplify both sides.

\(\displaystyle \frac{1}{4}y=1-\frac{1}{3}x\)

Multiply by four on both sides.

\(\displaystyle 4(\frac{1}{4}y)=4(1-\frac{1}{3}x)\)

Distribute both sides.

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

Rearrange the terms.

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

The slope is:  \(\displaystyle -\frac{4}{3}\)

To solve this problem you need to know the slope formula and set it up accordingly:

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

 \(\displaystyle \frac{1-0}{2-2}\)

This simplifies to:

\(\displaystyle \frac{1}{0}\)  and because 0 is in the denominator this slope is undefined.

Write the formula to find the slope given two points.

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

Substitute the given points into this formula.

\(\displaystyle m=\frac{6-9}{-3-6}\)

Simplify this fraction and reduce.

\(\displaystyle m=\frac{-3}{-9}= \frac{1}{3}\)

The slope equation is:

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

Plugging these points:

\(\displaystyle \frac{2-2}{4-3}\)

\(\displaystyle \frac{0}{1}=0\)

In order to find the slope, we must find the difference in \(\displaystyle y\) coordinates and divide this number by the difference between the \(\displaystyle x\) coordinates. 

\(\displaystyle (2,3)(4,5)\)

\(\displaystyle \text{Slope}=\frac{5-3}{4-2}=\frac{2}{2}=1\)

In order to find the slope, we must find the difference in \(\displaystyle y\) coordinates and divide this number by the difference between the \(\displaystyle x\) coordinates. 

\(\displaystyle (12,4)(6,6)\)

\(\displaystyle \text{Slope}=\frac{6-4}{6-12}=\frac{2}{-6}=-\frac{1}{3}\)