Question

Which of the following properly describe “slope”? Select the%C2%A0three that apply.(3 points) Responses riserun the fraction with numerator r i s e and denominator r u n runrise the fraction with numerator r u n and denominator r i s e x2−x1y2−y1 the fraction with numerator x sub 2 minus x sub 1 and denominator y sub 2 minus y sub 1 change in y-value over change in x-value change in y-value over change in x-value y2−y1x2−x1 the fraction with numerator y sub 2 minus y sub 1 and denominator x sub 2 minus x sub 1

Answer 1

The three correct descriptions of "slope" from the options provided are:

1. **the fraction with numerator rise and denominator run**: This is the basic definition of slope, often written as \( \text{slope} = \frac{\text{rise}}{\text{run}} \).

2. **change in y-value over change in x-value**: This is another way of defining slope, stating that it represents the change in the vertical direction (y) divided by the change in the horizontal direction (x).

3. **\( \frac{y_2 - y_1}{x_2 - x_1} \)**: This is the formal mathematical calculation of slope, where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

Thus, the correct responses are:
- the fraction with numerator rise and denominator run
- change in y-value over change in x-value
- \( \frac{y_2 - y_1}{x_2 - x_1} \)