Question
The slope of a line is -3.5. What is the simplified ratio of the vertical side length to the horizontal side length of each triangle formed?
-7/2
2/7
7/2
-2/7
-7/2
2/7
7/2
-2/7
Answers
GPT-4o mini
The slope of a line is defined as the ratio of the change in vertical position (rise) to the change in horizontal position (run). A slope of -3.5 can be expressed as a fraction:
\[
-3.5 = -\frac{7}{2}
\]
This means that for every horizontal movement of 2 units (run), the vertical movement (rise) is -7 units (which indicates a decrease, hence the negative sign).
Therefore, the simplified ratio of the vertical side length (rise) to the horizontal side length (run) is:
\[
\text{Vertical side length : Horizontal side length} = -7:2
\]
This can also be expressed as:
\[
-\frac{7}{2}
\]
Among the options provided, the correct simplified ratio is:
\[
\boxed{-\frac{7}{2}}
\]
\[
-3.5 = -\frac{7}{2}
\]
This means that for every horizontal movement of 2 units (run), the vertical movement (rise) is -7 units (which indicates a decrease, hence the negative sign).
Therefore, the simplified ratio of the vertical side length (rise) to the horizontal side length (run) is:
\[
\text{Vertical side length : Horizontal side length} = -7:2
\]
This can also be expressed as:
\[
-\frac{7}{2}
\]
Among the options provided, the correct simplified ratio is:
\[
\boxed{-\frac{7}{2}}
\]