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, we can see that the line passes through the points \((0, -5)\) and \((2, -1)\) (or other clear points, let's confirm with another pair like \((1, -3)\) and \((3, 1)\)). Let's take two points: let's choose \((0, -5)\) and \((2, -1)\).

Step2: Calculate the rise and run

Rise is the change in \(y\)-values: \(y_2 - y_1 = -1 - (-5) = -1 + 5 = 4\).
Run is the change in \(x\)-values: \(x_2 - x_1 = 2 - 0 = 2\).

Step3: Calculate the slope

Slope \(m=\frac{\text{rise}}{\text{run}}=\frac{4}{2} = 2\). Wait, let's check another pair. Let's take \((1, -3)\) and \((3, 1)\). Rise: \(1 - (-3)=4\), Run: \(3 - 1 = 2\), slope is \(\frac{4}{2}=2\). Alternatively, take \((2, -1)\) and \((3, 1)\): rise \(1 - (-1)=2\)? Wait no, maybe I made a mistake. Wait, looking at the line, when \(x = 0\), \(y=-5\); when \(x = 1\), \(y=-3\); \(x=2\), \(y=-1\); \(x=3\), \(y=1\); \(x=4\), \(y=3\); \(x=5\), \(y=5\); \(x=6\), \(y=7\); \(x=7\), \(y=9\). Wait, so from \((0, -5)\) to \((1, -3)\): rise is \(-3 - (-5)=2\), run is \(1 - 0 = 1\). So slope is \(\frac{2}{1}=2\). Wait, earlier I thought rise was 4, but with \(x\) change of 2, rise is 4, so \(\frac{4}{2}=2\). So the slope is 2.

Answer:

The slope of the line is \(\boxed{2}\)