How to find slope with fractions?

Steps to Solve

1. Identify the Coordinates We start by identifying two points on the line. For example, let’s say we have the points ( (x_1, y_1) ) and ( (x_2, y_2) ). For this example, let’s use ( (1/2, 3/4) ) and ( (1/4, 1/2) ).

2. Calculate the Change in y (Rise) The rise is calculated by finding the difference between the y-coordinates of the two points: $$ \text{Rise} = y_2 - y_1 $$

Substituting the values we have: $$ \text{Rise} = \frac{1}{2} - \frac{3}{4} $$

To perform the subtraction, we convert ( \frac{1}{2} ) to ( \frac{2}{4} ): $$ \text{Rise} = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4} $$

3. Calculate the Change in x (Run) Next, we calculate the run by finding the difference between the x-coordinates: $$ \text{Run} = x_2 - x_1 $$

Using our example points: $$ \text{Run} = \frac{1}{4} - \frac{1}{2} $$

Again, convert ( \frac{1}{2} ) to ( \frac{2}{4} ): $$ \text{Run} = \frac{1}{4} - \frac{2}{4} = -\frac{1}{4} $$

4. Calculate the Slope Now, we can find the slope ( m ) using the formula: $$ m = \frac{\text{Rise}}{\text{Run}} $$

Substituting the values we calculated: $$ m = \frac{-\frac{1}{4}}{-\frac{1}{4}} = 1 $$

5. Final Result The slope of the line between the two points is ( m = 1 ).