How to Find Slope Using the Formula

Equations- How it Works - Video

Example 1

Example 1:

We need to pick two points on the graph. It is easier if we pick two points that are intersected. Once we have done that then we can count. In the picture on the left we count up 2 spaces so the change in y (delta y) is positive 2. Then we count to the right 3 spaces so the change in x (delta x) is positive 3. To find the slope we need to put delta y over delta x and our result is 2/3.

What happens if we count the other way? In this case we count down 2 spaces so the change in y (delta y) is negative 2. Then we count to the left 3 spaces so the change in x (delta x) is negative 3. To find the slope we need to put delta y over delta x and our result is -2/-3. Since we are dividing by two negative numbers, the result is 2/3.

In the end it doesn't matter which way we count the slope will be the same.

Example 2

Example 2:

We need to pick two points on the graph. It is easier if we pick two points that are intersected. Once we have done that then we can count. In the picture on the left we count up 4 spaces so the change in y (delta y) is positive 4. Then we count to the right 6 spaces so the change in x (delta x) is positive 6. To find the slope we need to put delta y over delta x and our result is 4/6. Now we have to simplify by dividing each number by 2 so our final result is 2/3.

What happens if we count the other way? In this case we count down 4 spaces so the change in y (delta y) is negative 4. Then we count to the left 6 spaces so the change in x (delta x) is negative 6. To find the slope we need to put delta y over delta x and our result is -4/-6. Since we are dividing by two negative numbers, we have 4/6. Now we can divide each number by 2 so our final result is 2/3.

In the end it doesn't matter which way we count the slope will be the same.

Example 3

Example 3:

We need to pick two points on the graph. It is easier if we pick two points that are intersected. Once we have done that then we can count. In the picture on the left we count down 4 spaces so the change in y (delta y) is negative 4. Then we count to the right 3 spaces so the change in x (delta x) is positive 3. To find the slope we need to put delta y over delta x and our result is -4/3.

What happens if we count the other way? In this case we count up 4 spaces so the change in y (delta y) is positive 4. Then we count to the left 3 spaces so the change in x (delta x) is negative 3. To find the slope we need to put delta y over delta x and our result is -2/-3. Since we are dividing by two negative numbers, the result is -4/3.

In the end it doesn't matter which way we count the slope will be the same.

Example 4

Example 4:

We need to pick two points on the graph. It is easier if we pick two points that are intersected. Once we have done that then we can count. In the picture on the left we count down 8 spaces so the change in y (delta y) is negative 8. Then we count to the right 6 spaces so the change in x (delta x) is positive 6. To find the slope we need to put delta y over delta x and our result is -8/6. Now we have to simplify by dividing each number by 2 so our final result is -4/3.

What happens if we count the other way? In this case we count up 8 spaces so the change in y (delta y) is positive 8. Then we count to the left 6 spaces so the change in x (delta x) is negative 6. To find the slope we need to put delta y over delta x and our result is 8/-6. Since we are dividing by two negative numbers, we have 8/-6. Now we can divide each number by 2 so our final result is 4/-3, but we can rewrite it as -4/3, because negative sign can go on top or bottom.

In the end it doesn't matter which way we count the slope will be the same.

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