Question

1. the points (2.1, -4.2) and (2.5, -5) form a proportional relationship. what is the slope of the line that passes through these two points?

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(2.1, - 4.2)\) and \((x_2, y_2)=(2.5, - 5)\).

Step2: Substitute values into formula

Substitute \( x_1 = 2.1\), \( y_1=-4.2\), \( x_2 = 2.5\), \( y_2=-5\) into the slope formula:
\( m=\frac{-5-(-4.2)}{2.5 - 2.1}=\frac{-5 + 4.2}{0.4}=\frac{-0.8}{0.4}\)

Step3: Simplify the fraction

\(\frac{-0.8}{0.4}=- 2\)

Answer:

\(-2\)