To determine the slope of a line, you need to have an understanding of how the change in the vertical direction compares to the change in the horizontal direction between two points on the line. This is commonly referred to as the "rise" over the "run."
1. Rise refers to the change in the y-values (vertical change) between two points.
2. Run refers to the change in the x-values (horizontal change) between the same two points.
The formula to calculate the slope (often denoted as [tex]\( m \)[/tex]) of a line is:
[tex]\[ \text{slope} = \frac{\text{rise}}{\text{run}} \][/tex]
- Option A suggests that slope [tex]\( = \frac{\text{ run }}{\text { rise }}\)[/tex]. This is incorrect because it inverts the relationship.
- Option B suggests that slope [tex]\( = \text{ run } \bullet \text{ rise }\)[/tex]. This is also incorrect because slope involves a division, not a multiplication.
- Option C suggests that slope [tex]\( = \text{ rise } - \text{ run }\)[/tex]. This is incorrect because slope involves division, not subtraction.
- Option D suggests that slope [tex]\( = \frac{\text{ rise }}{\text { run }}\)[/tex]. This is correct as it accurately represents the relationship needed to compute the slope.
Thus, the correct relationship used to find the slope of a line is:
[tex]\[ \text{slope} = \frac{\text { rise }}{\text{ run }} \][/tex]
Therefore, the answer is:
D. slope [tex]\( = \frac{\text{ rise }}{\text { run }}\)[/tex]
