Question

draw a line representing the
ise\ and a line representing the
un\ of the line. state the slope of the line in simplest form.
click twice to plot each segment.
click a segment to delete it.

Explanation:

Step1: Identify two points on the line

Looking at the graph, the line passes through \((0, 2)\) (the y - intercept) and \((1, 0)\) (we can also use other points, but these are easy to identify).

Step2: Calculate the rise and run

The formula for slope \(m=\frac{\text{rise}}{\text{run}}\), where rise is the change in \(y\) (\(\Delta y\)) and run is the change in \(x\) (\(\Delta x\)). For the points \((0, 2)\) and \((1, 0)\), \(\Delta y=0 - 2=- 2\) and \(\Delta x = 1-0 = 1\).

Step3: Calculate the slope

Using the slope formula \(m=\frac{\Delta y}{\Delta x}\), we substitute \(\Delta y=-2\) and \(\Delta x = 1\). So \(m=\frac{-2}{1}=-2\).
(For drawing the rise and run: To draw the rise, we draw a vertical line from one point to the level of the other point (showing the change in \(y\)), and to draw the run, we draw a horizontal line from the end of the rise to the other point (showing the change in \(x\)). For example, from \((0, 2)\), the rise would be a vertical line down 2 units (since \(y\) decreases) to \(y = 0\), and then the run would be a horizontal line to the right 1 unit to \((1, 0)\).)

Answer:

The slope of the line is \(-2\)