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 \((0, 1)\) and \((2, -9)\) (or other clear points, but let's use these for calculation). Wait, actually, let's check the intercepts. The line passes through the origin? Wait, no, looking at the graph, when \(x = 0\), \(y = 1\)? Wait, maybe better to take two points: let's take \((0, 1)\) and \((1, -4)\)? Wait, no, let's do it properly. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's pick two points: let's say \((0, 1)\) and \((2, -9)\)? Wait, no, maybe I made a mistake. Wait, the line goes through (0,1) and (1, -4)? Wait, no, let's check the grid. Let's take two points: (0, 1) and (1, -4)? Wait, no, the rise is the change in y, run is change in x. Let's take two points: let's say from (0, 1) to (2, -9)? No, that's not right. Wait, maybe the line passes through (0,0) and (1, -5)? Wait, looking at the graph, the line seems to have a steep negative slope. Let's take two points: (0, 1) and (1, -4)? Wait, no, let's calculate the slope. Let's take two points: (0, 1) and (2, -9). Then \(y_2 - y_1=-9 - 1=-10\), \(x_2 - x_1=2 - 0 = 2\). Then slope \(m=\frac{-10}{2}=-5\). Wait, or maybe (0,0) and (1, -5)? Wait, maybe the correct two points are (0, 0) and (1, -5)? Wait, the graph shows the line passing through the origin? Wait, the x-axis and y-axis intersect at (0,0), and the line passes through (0,0) and (2, -10)? Then \(y_2 - y_1=-10 - 0=-10\), \(x_2 - x_1=2 - 0 = 2\), so slope \(m=\frac{-10}{2}=-5\). So the rise is -10 (since it's decreasing) and run is 2, but simplified, slope is -5.

Step2: Calculate the slope

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line, say \((0, 0)\) and \((2, -10)\). Then \(y_2 - y_1=-10 - 0=-10\), \(x_2 - x_1=2 - 0 = 2\). Then \(m=\frac{-10}{2}=-5\). Alternatively, take \((1, -5)\) and \((0, 0)\), then \(m=\frac{-5 - 0}{1 - 0}=-5\). So the slope is -5. The rise would be -10 (for a run of 2) or -5 (for a run of 1), but the simplest form of the slope is -5.

Answer:

The slope of the line is \(-5\). (For drawing the rise and run: from a point on the line, draw a vertical line for rise (downward if negative) and horizontal line for run (rightward), then calculate slope as rise over run.)