For each equation, solve for \(\displaystyle y\) and express in the slope-intercept form \(\displaystyle y=mx + b\). The coefficient of \(\displaystyle x\) will be the slope.

\(\displaystyle 9x+ y = 81\)

\(\displaystyle 9x+ y -9x = 81 -9x\)

\(\displaystyle y = -9x + 81\)

\(\displaystyle m = -9\)

\(\displaystyle x+ 9 y = 81\)

\(\displaystyle x+ 9 y - x = 81 - x\)

\(\displaystyle 9 y = - x + 81\)

\(\displaystyle \frac{9 y}{9} = \frac{ - x + 81 }{9}\)

\(\displaystyle y = - \frac{1}{9}x + 9\)

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

\(\displaystyle x = 9 y + 81\)

\(\displaystyle 9x - 81 = y + 81 - 81\)

\(\displaystyle y = 9x - 81\)

\(\displaystyle m = 9\)

\(\displaystyle x = 9 y + 81\)

\(\displaystyle x - 81= 9 y + 81 - 81\)

\(\displaystyle x - 81= 9 y\)

\(\displaystyle \frac{x - 81}{9}= \frac{9 y }{9}\)

\(\displaystyle y = \frac{ 1}{9}x - 9\)

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

\(\displaystyle x = 9 y + 81\) is graphed by a line with slope \(\displaystyle m= \frac{ 1}{9}\) and is the correct choice.

The equation given should be written in slope-intercept form, or \(\displaystyle y=mx+b\) format.

The \(\displaystyle m\) in the slope-intercept equation represents the slope.

\(\displaystyle -2x+2y=1\)

Add \(\displaystyle 2x\) on both sides of the equation.

\(\displaystyle 2y = 2x + 1\)

Divide by two on both sides of the equation to isolate y.

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

Therefore, the slope is 1.

Write the formula for the slope.

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

We can select any point to be \(\displaystyle (x_1, y_1)\) and vice versa.

\(\displaystyle m = \frac{4-(-5)}{-6-1} = -\frac{9}{7}\)

The answer is:  \(\displaystyle -\frac{9}{7}\)

We will need to group the x variables on one side of the equation and the y-variable on the other.

Add \(\displaystyle 9y\) on both sides.

\(\displaystyle -7x+(9y) = -9y-x+(9y)\)

\(\displaystyle -7x+9y = -x\)

Add \(\displaystyle 7x\) on both sides.

\(\displaystyle -7x+9y+(7x) = -x+7x\)

\(\displaystyle 9y = 6x\)

Divide both sides by 9.

\(\displaystyle \frac{9y }{9}=\frac{ 6x}{9}\)

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

The slope is \(\displaystyle \frac{2}{3}\).

To find the slope, rewrite the equation in slope intercept form.

\(\displaystyle y=mx+b\)

Add \(\displaystyle 2y\) on both sides.

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

\(\displaystyle y=-x\)

This is the same as:  \(\displaystyle y=-1x+0\)

This means that the slope is \(\displaystyle -1\).

The answer is:  \(\displaystyle -1\)

Simplify the equation so that it is in slope-intercept format.

\(\displaystyle y=mx+b\)

\(\displaystyle y=-9x-x+2 = -10x+2\)

The simplified equation is:  \(\displaystyle y=-10x+2\)

The slope is:  \(\displaystyle -10\)

Recall that slope is calculated as:

\(\displaystyle \frac{rise}{run}\)

This could be represented, using your two points, as:

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

Based on your data, this would be:

\(\displaystyle \frac{-10-5}{9-4}=\frac{-15}{5}=-3\)

There are two ways that you can do a problem like this.  First you could calculate the slope from two points.  You would do this by first choosing two values and then using the slope formula, namely:

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

This could take some time, however.  You could also solve it by using the slope intercept form of the equation, which is:

\(\displaystyle y=mx+b\)

If you get your equation into this form, you just need to look at the coefficient \(\displaystyle m\).  This will give you all that you need for knowing the slope.

Your equation is:

\(\displaystyle 3x+4y=10\)

What you need to do is isolate \(\displaystyle y\):

\(\displaystyle 4y=10-3x\)

Notice that this is the same as:

\(\displaystyle 4y=-3x+10\)

The next operation confuses some folks.  However, it is very simple.  Just divide everything by \(\displaystyle 4\).  This gives you:

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

You do not need to do anything else.  The slope is \(\displaystyle \frac{-3}{4}\).

To determine the slope, we will need the equation in slope-intercept form.

\(\displaystyle y=mx+b\)

Subtract \(\displaystyle 2x\) from both sides.

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

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

Divide by negative three on both sides.

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

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

The slope is:  \(\displaystyle \frac{2}{3}\)

There are two ways that you can do a problem like this.  First you could calculate the slope from two points.  You would do this by first choosing two values and then using the slope formula, namely:

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

This could take some time, however.  You could also solve it by using the slope intercept form of the equation, which is:

\(\displaystyle y=mx+b\)

If you get your equation into this form, you just need to look at the coefficient \(\displaystyle m\).  This will give you all that you need for knowing the slope.

Your equation is:

\(\displaystyle 11x-44y=10\)

What you need to do is isolate \(\displaystyle y\):

\(\displaystyle -44y=10-11x\)

Notice that this is the same as:

\(\displaystyle -44y=-11x+10\)

The next operation confuses some folks.  However, it is very simple.  Just divide everything by \(\displaystyle -44\).  This gives you:

\(\displaystyle y=\frac{-11}{-44}x+\frac{10}{-44}\)

Now, take the coefficient from \(\displaystyle x\).  It is \(\displaystyle \frac{-11}{-44}\).  

You can reduce this to\(\displaystyle \frac{1}{4}\).  This is your slope.