Question

1. consider the given line.

a. use a slope triangle to find the slope of the line.
b. use the slope formula to find the slope of the line.

Explanation:

Step1: Identify two points on the line

Let's take two points on the line, say (0, 2) and (2, 0).

Step2: Use the slope - triangle method

The slope triangle shows that as we move from (0, 2) to (2, 0), we go down 2 units (vertical change, $\Delta y$) and right 2 units (horizontal change, $\Delta x$). The slope $m=\frac{\Delta y}{\Delta x}$. So, $m=\frac{0 - 2}{2-0}=\frac{- 2}{2}=-1$.

Step3: Use the slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(2,0)$, we substitute into the formula: $m=\frac{0 - 2}{2 - 0}=\frac{-2}{2}=-1$.

Answer:

a. The slope of the line using the slope - triangle method is - 1.
b. The slope of the line using the slope formula is - 1.