Question

1. lyn was trying to find the slope ratio for the triangle at right, and she says the answer is $\frac{delta y}{delta x}=2.675$. kristi claims that cannot be correct. who is right? how do you know?

Explanation:

Step1: Recall slope - ratio concept

The slope ratio $\frac{\Delta y}{\Delta x}$ represents the vertical change over the horizontal change. Slope values can be positive, negative, zero or undefined. However, the slope ratio is a real - number value and should be in a simplified form. A value like $2.6\overline{75}$ is a non - standard way to represent a slope ratio. Usually, slopes are given as fractions, decimals in a non - repeating form (if rational) or as irrational numbers in radical form (if applicable).

Step2: Determine who is right

Kris is right. A slope ratio should be in a proper numerical form. A non - standard repeating decimal like $2.6\overline{75}$ is not an appropriate way to express the slope of a line. The slope should be either a fraction, a simple non - repeating decimal (for rational slopes) or an exact value (like $\sqrt{2}$ for some geometric cases).

Answer:

Kris is right because the slope ratio should be in a proper numerical form and $2.6\overline{75}$ is a non - standard way to represent it.