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: Identify slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Assign values

Let $(x_1,y_1)=(2.1,-4.2)$ and $(x_2,y_2)=(2.5,-5)$. Then $m=\frac{-5-(-4.2)}{2.5 - 2.1}$.

Step3: Simplify numerator and denominator

The numerator is $-5+4.2=-0.8$, and the denominator is $2.5 - 2.1 = 0.4$. So $m=\frac{-0.8}{0.4}$.

Step4: Calculate the slope

$m=- 2$.

Answer:

$-2$