Slope of a Line
How to find the slope of a line that passes through two points: formula, 4 examples, and their solutions.
Formula
The slope means the ratio of
[change of y]/[change of x].
If a line passes through (x1, y1) and (x2, y2),
(change of x) = x2 - x1,
(change of y) = y2 - y1.
So the slope of the line, m, is
m = (y2 - y1)/(x2 - x1).
ExampleSlope: (1, 1) and (3, 5)
So the slope of the line, m, is 2.
As you can see,
if a line goes ↗,
then the slope of the line is plus.
Draw a line that passes through
(1, 1) and (3, 5).
The change of x is
3 - 1 = 2.
The change of y is
5 - 1 = 4.
So the change of x is 2.
And the change of y is 4.
Then the slope, m, is
m = 4/2.
4/2 = 2
So the slope of the line, m, is 2.
As you can see,
if a line goes ↗,
then the slope of the line is plus.
ExampleSlope: (-4, 1) and (1, -2)
So the slope of the line, m, is -3/5.
As you can see,
if a line goes ↘,
then the slope of the line is minus.
Draw a line that passes through
(-4, 1) and (1, -2).
The change of x is
1 - (-4) = 1 + 4 = 5.
The change of y is
-2 - 1 = -3.
So the change of x is 5.
And the change of y is -3.
Then the slope, m, is
m = (-3)/5.
(-3)/5 = -3/5
So the slope of the line, m, is -3/5.
As you can see,
if a line goes ↘,
then the slope of the line is minus.
ExampleSlope: (-1, 2) and (5, 2)
So the slope of the line, m, is 0.
As you can see,
if a line is →,
then the slope of the line is 0.
Draw a line that passes through
(-1, 2) and (5, 2).
The change of x is
5 - (-1) = 5 + 1 = 6.
The change of y is
2 - 2 = 0.
Then the slope, m, is
m = 0/6.
If the numerator is 0,
then the fraction is 0.
So 0/6 = 0.
So the slope of the line, m, is 0.
As you can see,
if a line is →,
then the slope of the line is 0.
ExampleSlope: (1, 2) and (1, -3)
So the answer is [no slope].
As you can see,
if a line is ↕,
then the line has no slope.
Draw a line that passes through
(1, 2) and (1, -3).
The change of x is
1 - 1 = 0.
The change of y is
-3 - 2 = -5.
Then the slope, m, is
m = (-5)/0.
The denominator of a fraction cannot be 0.
So (-5)/0 doesn't make sense.
So the line has no slope.
So the answer is [no slope].
As you can see,
if a line is ↕,
then the line has no slope.