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

From the graph, let's take two points on the line, say \((0, -3)\) and \((2, 0)\) (we can also use other points, but these are clear).

Step2: Calculate rise and run

Rise is the change in \(y\), so \(0 - (-3)=3\). Run is the change in \(x\), so \(2 - 0 = 2\)? Wait, no, maybe better to take another pair. Wait, looking at the line, when \(x = 0\), \(y=-3\); when \(x = 1\), \(y=-1\)? Wait, maybe I misread. Wait, let's check the y-intercept. The line crosses the y-axis at \((0, -3)\)? Wait, no, maybe the y-intercept is \((0, -3)\) and when \(x = 2\), \(y = 0\)? Wait, no, let's recalculate. Wait, slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two clear points: let's say \((0, -3)\) and \((1, -1)\)? Wait, no, maybe the correct points are \((0, -3)\) and \((2, 1)\)? Wait, no, maybe I made a mistake. Wait, the line goes through \((0, -3)\) and \((2, 1)\)? No, let's look at the grid. Wait, the y-axis has marks, let's see: from \((0, -3)\) to \((2, 1)\)? No, maybe the rise is 2 and run is 1? Wait, no, let's do it properly. Let's take two points: let's say \((0, -3)\) and \((1, -1)\). Then rise is \(-1 - (-3)=2\), run is \(1 - 0 = 1\). Wait, no, that would make slope 2. Wait, maybe the points are \((0, -3)\) and \((2, 1)\): rise is \(1 - (-3)=4\), run is \(2 - 0 = 2\), slope \(4/2 = 2\)? No, that can't be. Wait, maybe I messed up the points. Wait, let's look again. The line: when \(x = 0\), \(y=-3\); when \(x = 1\), \(y=-1\); when \(x = 2\), \(y = 1\); when \(x = 3\), \(y = 3\). Ah, so from \((0, -3)\) to \((1, -1)\): rise is \(-1 - (-3)=2\), run is \(1 - 0 = 1\), so slope is \(2/1 = 2\)? Wait, no, wait \((0, -3)\) to \((1, -1)\): change in y is \(2\), change in x is \(1\), so slope is \(2\). Wait, but maybe the correct points are \((0, -3)\) and \((2, 1)\): change in y is \(4\), change in x is \(2\), slope \(4/2 = 2\). So the slope is 2. Wait, but let's confirm with the formula. Let's take two points: \((0, -3)\) and \((1, -1)\). Then \(m=\frac{-1 - (-3)}{1 - 0}=\frac{2}{1}=2\). So the slope is 2. Wait, but maybe I made a mistake in the points. Wait, the line: when x increases by 1, y increases by 2. So rise is 2, run is 1, slope is 2.

Step3: State the slope

Using the slope formula \(m = \frac{\text{rise}}{\text{run}}\), and from the points, the slope is 2. Wait, but let's check again. Wait, maybe the two points are \((0, -3)\) and \((2, 1)\): rise is \(1 - (-3)=4\), run is \(2 - 0 = 2\), slope \(4/2 = 2\). Yes, so the slope is 2.

Answer:

The slope of the line is \(\boldsymbol{2}\) (For drawing the rise and run: from a point on the line, draw a vertical line for rise (change in y) and horizontal line for run (change in x), then calculate slope as rise over run).