Question

draw a line representing the rise and a line representing the run 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:

To determine the slope of the line, we first identify two points on the line. From the graph, let's assume two clear points: let's say the y - intercept is (0, 6) and another point where the line crosses the x - axis is (2, 0) (we can also use other points, but these are easy to identify).

Step 1: Recall the slope formula

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Step 2: Identify the coordinates of two points

Let \((x_1,y_1)=(0,6)\) and \((x_2,y_2)=(2,0)\)

Step 3: Calculate the rise and run

The "rise" is the change in \(y\) - values, so \(y_2 - y_1=0 - 6=- 6\)
The "run" is the change in \(x\) - values, so \(x_2 - x_1=2 - 0 = 2\)

Step 4: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-6}{2}=- 3\)

We can also think of rise over run. If we take two other points, for example, if we move from a higher point to a lower point, the rise is negative (since we are moving down) and the run is positive (if we move to the right).

If we consider the two points \((0,6)\) and \((1,3)\) (by looking at the grid), the rise \(y_2 - y_1=3 - 6=-3\) and the run \(x_2 - x_1=1 - 0 = 1\), then the slope \(m=\frac{-3}{1}=-3\)

Answer:

The slope of the line is \(-3\)