Finding the Slope of a Line

In most upper level math courses, you will be asked to find the slope of a line, because it is an important part of graphing a line. There are many different ways to find the slope, depending on the information you are given.

Method One

This is the best method to find the slope when you are given two sets of points on a line. To solve this way, you are going to use the formula m=(y₂-y₁)/(x₂-x₁), where m is the slope, and (x₁,y₁) and (x₂,y₂). Find the slope of a line that passes through the point (3,4) and (6,8). The first step is plugging the numbers into the equation for finding slope, then solve the equation.

x₁=3, y₁=4, x₂=6, y₂=8
m=(y₂-y₁)/(x₂-x₁),
m=(8-4)/(6-3)
m=4/3

The slope of the equation that passes through the point (3,4) and (6,8) is 3/4.

Method Two

This method is used when you are giving the equation of a line, and you want to find the slope. This method is much easier than the other. The first step is to get the equation into slope-intercept form. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Find the slope of the equation 4y+6x=8x+16.

You will first have to move all the x variables to the opposite side of the equation as the y variable. Because the 6x is being added, we are going to have to do the opposite operation, which is addition, to move it to the other side.

4y+6x=8x+16
4y+6x-6x=8x+16-6x
4y=8x+16-6x

The next step is combining like terms.

4y=8x+16-6x
4y=2x+16

Now, you will have to get rid of the four being multiplied by the y. Because the opposite operation of multiplication is division, we are going to divide by four on both sides.

4y=2x+16
4y/4=(2x+16)/4
y=2/4x+16/4

Now simplify.

y=2/4x+16/4
y=1/2x+4

Now we have our equation in slope-intercept from. From here, finding the slope of the line is very easy. We know that y=mx+b where m is slope and b is y-intercept, so using the formula, we can come to the conclusion that the slope of our line is 1/2.

Good luck and happy solving!