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 the origin \((0,0)\) and another point, say \((1, -4)\) (or we can use another pair, but let's check the slope formula). Wait, actually, let's take two clear points. Let's see, from the graph, when \(x = 0\), \(y = 0\), and when \(x = 1\), \(y=-4\)? Wait, no, maybe better to take two points with integer coordinates. Let's see, the line goes through \((0,0)\) and \((1, -4)\)? Wait, no, let's check the rise and run. The slope formula is \(m=\frac{\text{rise}}{\text{run}}=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: \((0,0)\) and \((1, -4)\)? Wait, no, maybe \((0,0)\) and \((-1, 4)\)? Wait, no, let's look at the direction. The line is decreasing, so slope is negative. Let's take two points: let's say \((0,0)\) and \((1, -4)\)? Wait, no, maybe \((0,0)\) and \((2, -8)\)? Wait, no, maybe I made a mistake. Wait, the line in the graph: when \(x = 0\), \(y = 0\), and when \(x = 1\), \(y=-4\)? Wait, no, let's count the rise and run. Let's take two points: \((0,0)\) and \((1, -4)\). Then rise is \(y_2 - y_1=-4 - 0=-4\), run is \(x_2 - x_1=1 - 0 = 1\). Wait, but maybe another pair. Wait, maybe \((0,0)\) and \((-1, 4)\). Then rise is \(4-0 = 4\), run is \(-1 - 0=-1\), but slope is \(\frac{4}{-1}=-4\). So the slope is \(-4\). Wait, let's confirm. The slope formula is \(m=\frac{\Delta y}{\Delta x}\). Let's take two points: \((0,0)\) and \((1, -4)\). Then \(\Delta y=-4 - 0=-4\), \(\Delta x=1 - 0 = 1\), so \(m=\frac{-4}{1}=-4\). So the slope is \(-4\).

Step2: Calculate the slope

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), with points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1, -4)\), we get \(m=\frac{-4 - 0}{1 - 0}=\frac{-4}{1}=-4\). So the slope is \(-4\).

Answer:

The slope of the line is \(\boxed{-4}\)