The slope can be found between two points by finding the change in $\displaystyle y$ values divided by the change in $\displaystyle x$ values.

$\displaystyle slope=\frac{\Delta y}{\Delta x}$

which is often referred to as rise over run,

You can actually use any two points along the line to find the slope as long as the line is linear (straight line). Taking the end points since they are given is a convenient way of doing it.

$\displaystyle slope=\frac{\Delta y}{\Delta x}=\frac{(B)_{y}-(A)_{y}}{(B)_{x}-(A)_{x}}$

$\displaystyle slope=\frac{-1-3}{3-(-2)}=\frac{-4}{5}$

So the slope of this line segment is $\displaystyle -0.8$

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

$\displaystyle y = mx+ b$

where $\displaystyle m$ is the slope.

So, in the equation

$\displaystyle -8y = 24x - 16$

we will solve for y and get it by itself.  To do that, we will divide each term by $\displaystyle -8$.

$\displaystyle \frac{-8y}{-8} = \frac{24x}{-8} - \frac{16}{-8}$

$\displaystyle y = -3x + 2$

Looking at this equation, we can see $\displaystyle -3$ is the slope.

Write the formula for slope.

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

Either choice will yield the same slope.  Let's use the first equation.

$\displaystyle m=\frac{y_1-y_2}{x_1-x_2} = \frac{8-(-2)}{2-3}$

Simplify to find the slope.

$\displaystyle \frac{8-(-2)}{2-3} =\frac{10}{-1}=-10$

The slope $\displaystyle (m)$ of a line can be solved if you know at least two points that fall on the line using the following equation:

$\displaystyle m = \frac{y1-y2}{x1-x2}$

The $\displaystyle y$ coordinates are always written second when looking at coordinate pairs, and therefore the $\displaystyle x$ coordinates are first. We can thus insert our given points into this equation:

$\displaystyle m = \frac{4-8}{9-12}$

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

$\displaystyle m = \frac{4}{3}$

Find the slope of the line connecting the following two points:

$\displaystyle (99,156)$ $\displaystyle (44,101)$

Find slope with the following formula:

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

$\displaystyle m=\frac{156-101}{99-44}=\frac{55}{55}=1$

so our slope is simply 1

In order to find the slope, we need to put the following equation in slope intercept form.

$\displaystyle y=mx+b$

The $\displaystyle m$ represents the slope.

Subtract $\displaystyle 2x$ on both sides.

$\displaystyle 2x-3y-2x=19-2x$

Simplify the left side and reorganize the right.

$\displaystyle -3y=-2x+19$

Divide by negative three on both sides.

$\displaystyle \frac{-3y}{-3}=\frac{-2x+19}{-3}$

Simplify both sides.

$\displaystyle y=\frac{2}{3}x-\frac{19}{3}$

The slope is $\displaystyle \frac{2}{3}$.

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

$\displaystyle 2x+3y=5$

$\displaystyle 3y=-2x+5$

$\displaystyle y=\frac{-2}{3}x+\frac{5}{3}$

The slope is the number in front of the "x" which in this case is -2/3

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

$\displaystyle x-y=6$

$\displaystyle -y=-x+6$

$\displaystyle y=x-6$

The slope is the number in front of the "x" which in this case is 1

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

$\displaystyle 3x+y=4$

$\displaystyle y=-3x+4$

The slope is the number in front of the "x" which in this case is -3

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

$\displaystyle -x+2y=2$

$\displaystyle 2y=x+2$

$\displaystyle y=\frac{1}{2}x+1$

The slope is the number in front of the "x" which in this case is 1/2