

How to find the slope of a line.
The slope of a line characterizes the general direction in which a line points. To find the slope, you divide the difference of the ycoordinates of a point on a line by the difference of the xcoordinates.
Formula to find the slope of a lineExample One The slope of a line going through the point (1,2) and the point (4,3) is 1/3.Example 2 of the Slope of A line The slope of a line through the points (3, 4) and (5, 1) is 3/2 because every time that the line goes down by 3(the change in y or the rise) the line moves to the right (the run) by 2. Does it matter which point you start with?There is only one way to know! Let's try to find the slope of a line through the points (4,3) and (1,2) .First we'll start with one point and then we'll start with the other.First, let's start with the point (4,3) $$slope= \frac{y_{2}y_{1}}{x_{2}x_{1}} = \frac{32}{41} =\frac{1}{3} $$ Now, let's start with the point (1,2) $$slope= \frac{y_{2}y_{1}}{x_{2}x_{1}} = \frac{23}{14} =\frac{1}{3}=\frac{1}{3} $$ And the Answer is...It does not matter which point you put first. You can start with (4,3) or with (1,2) and, either way, you end with the exact same number! $\frac{1}{3} $This Page: Do any two points determine the slope of a line? Practice Problems  Slope of Vertical a Line  Slope of Horizontal Line Related pages: How to Find Slope from Graph
Video Tutorial on the Slope of a Line
Slope of vertical and horizontal lines
Do any two points on a line have the same slope?And the answer is...Yes, and this is a fundamental point to remember about calculating slope.Every line has a consistent slope. In other words, the slope of a line never changes. This fundamental idea means that you can choose ANY two points on a line to find the slope. This should intuitively make sense with your own understanding of a straight line. After all, if the slope of a line could change, then it would be a zigzag line and not a straight line, as you can see in the picture below. This Page: Do any two points determine the slope of a line? Practice Problems  Slope of Vertical a Line  Slope of Horizontal Line
Practice Problems
WARNING! Can you catch the error in the following problem Jennifer was trying to find the slope that goes through the points $$(\color{blue}{1},\color{red}{3})$$ and $$ (\color{blue}{2}, \color{red}{6})$$ . She was having a bit of trouble applying the slope formula, tried to calculate slope 3 times, and she came up with 3 different answers. Can you determine the correct answer?
Practice Problem 5) What is the slope of a line that goes through the points (10,3) and (7 , 9) ?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\=
\frac{93}{710}= \frac{6}{3} = 2
$$
Or, you can start with the other point $$\frac{39}{107}=\frac{6}{3} = 2 $$ Practice Problem 6) A line passes through (4, 2) and (4 , 3). What is its slope?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\
= \frac{2  3}{4 4} =
\frac{5}{ \color{red}{0}}= \text{undefined}$$
Whenever the run of a line is zero, the slope is undefined. This is because there is a zero in the denominator of the slope! Any the slope of any vertical line is undefined . Practice Problem 7) A line passes through (2, 10) and (8 , 7). What is its slope?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\
\frac{10  7}{2  8} = \frac{3}{6} = \frac{1}{2} $$
Or, you can start with the other point $$\frac{7  10}{82} = \frac{3}{6} == \frac{1}{2}$$ Practice Problem 8) A line passes through (7,3) and (8 , 5). What is its slope?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\
\frac{ 53}{87} = \frac{2}{1} = 2
$$
Or $$ \frac{ 35}{78} = \frac{2}{1} = 2 $$ Practice Problem 9) A line passes through (12,11) and (9 , 5). What is its slope?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\
\frac{ 11  5}{129}= \frac{6}{3}=2
$$
Or : $$ \frac{ 511}{912}= \frac{6}{3}= 2 $$ Practice Problem 10) What is the slope of a line that goes through (4, 2) and (4, 5)?
$$
\frac{rise}{run}= \frac{y_{2}y_{1}}{x_{2}x_{1}}
\\
\frac{ 2  5}{44}= \frac{ 3}{\color{red}{0}}= undefined
$$
Slope Practice  Problem Generator
You can practice solving this sort of problem as much as you would like with the slope problem generator below. It will randomly generate numbers and ask for the slope of the line through those two points. You can chose how large the numbers will be by adjusting the difficulty level. Answer
Generate New Slope Problem
This Page: Do any two points determine the slope of a line? Practice Problems  Slope of Vertical a Line  Slope of Horizontal Line Related pages: How to Find Slope from Graph  Erroneous Slope  images  Slope from Graph  Erroneous Slope Worksheet on Slope Of A Line Slope Formula Calculator (Free online tool calculates slope given 2 points) 