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 \((0, -5)\) and \((2, 0)\) (or other clear points, but let's use these for simplicity).

Step2: Calculate the rise

Rise is the change in \(y\)-values. So, \(y_2 - y_1 = 0 - (-5) = 5\).

Step3: Calculate the run

Run is the change in \(x\)-values. So, \(x_2 - x_1 = 2 - 0 = 2\). Wait, no, maybe better to take another pair. Wait, actually, let's check the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Wait, maybe the line has a steeper slope. Wait, looking at the graph, when \(x = 1\), \(y=-0\)? Wait, no, maybe the two points are \((1, -0)\)? Wait, no, let's re - examine. Wait, the line passes through \((0, -5)\) and \((1, 0)\)? Wait, no, the slope calculation: Let's take two points. Let's say the line goes through \((0, -5)\) and \((2, 5)\)? Wait, no, the graph shows that when \(x = 0\), \(y=-5\), and when \(x = 1\), \(y = 0\)? Wait, no, maybe I made a mistake. Wait, the correct way: The slope \(m=\frac{\text{rise}}{\text{run}}\), where rise is vertical change and run is horizontal change. Let's take two points on the line. Let's say point \(A=(0, -5)\) and point \(B=(1, 0)\). Then rise \(=0 - (-5)=5\), run \(=1 - 0 = 1\)? No, that can't be. Wait, maybe the line passes through \((0, -5)\) and \((2, 5)\). Then rise \(=5-(-5)=10\), run \(=2 - 0 = 2\), so slope \(=\frac{10}{2}=5\)? Wait, no, maybe the correct two points are \((0, -5)\) and \((1, 0)\). Then rise \(=0 - (-5)=5\), run \(=1 - 0 = 1\), slope \(=\frac{5}{1}=5\). Wait, but let's check again. Wait, the graph: the line crosses the \(y\)-axis at \((0, -5)\) and when \(x = 1\), \(y = 0\), when \(x = 2\), \(y = 5\), etc. So the rise between \((0, -5)\) and \((1, 0)\) is \(0-(-5) = 5\) (up 5 units), and the run is \(1 - 0=1\) (right 1 unit). So slope \(m=\frac{5}{1}=5\).

Step4: State the slope

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), with two points \((x_1,y_1)=(0, - 5)\) and \((x_2,y_2)=(1,0)\), we have \(m=\frac{0 - (-5)}{1 - 0}=\frac{5}{1}=5\).

Answer:

The slope of the line is \(5\).

(Note: For drawing the rise and run, the "rise" line is a vertical line segment between two points on the line, and the "run" line is a horizontal line segment between the same two points. For example, from \((0, -5)\) to \((1,0)\), the rise line is vertical from \((0, -5)\) to \((0,0)\) (wait, no, that's not right). Wait, no, the rise is the vertical change, so from \((0, -5)\) to \((1,0)\), the rise is the vertical segment from \((0, -5)\) to \((0,0)\) (length 5) and the run is the horizontal segment from \((0,0)\) to \((1,0)\) (length 1). Then the slope is \(\frac{5}{1}=5\).)