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

From the graph, we can see that the line passes through \((0, 4)\) and \((-6, 0)\) (or other pairs, but let's use these for calculation).

Step2: Calculate the rise and run

Rise is the change in \(y\)-values: \(y_2 - y_1 = 4 - 0 = 4\) (if we take \((0, 4)\) as \((x_2,y_2)\) and \((-6, 0)\) as \((x_1,y_1)\), or we can also consider the direction. Alternatively, using two points \((x_1,y_1)=(-6,0)\) and \((x_2,y_2)=(0,4)\), rise \(= y_2 - y_1 = 4 - 0 = 4\), run \(= x_2 - x_1 = 0 - (-6) = 6\).

Step3: Calculate the slope

Slope \(m=\frac{\text{rise}}{\text{run}}=\frac{4}{6}=\frac{2}{3}\)? Wait, no, wait. Wait, maybe I took the wrong points. Wait, looking at the graph, when \(x = 0\), \(y = 4\)? Wait, no, wait the \(y\)-intercept: looking at the graph, the line crosses the \(y\)-axis at \(y = 4\)? Wait, no, maybe I misread. Wait, let's check another pair. Let's take the \(x\)-intercept: when \(y = 0\), \(x=-6\)? Wait, no, the \(x\)-intercept seems to be at \(x=-6\)? Wait, no, looking at the graph, the line crosses the \(x\)-axis at \(x = -6\)? Wait, no, the arrow on the left: when \(y = 0\), \(x=-6\)? Wait, no, let's take two clear points. Let's take \((0, 4)\) and \((3, 6)\)? Wait, no, maybe the correct points are \((0, 4)\) and \((6, 8)\)? Wait, no, let's use the formula for slope. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: let's say \((-6, 0)\) and \((0, 4)\). Then \(y_2 - y_1 = 4 - 0 = 4\), \(x_2 - x_1 = 0 - (-6) = 6\), so slope \(=\frac{4}{6}=\frac{2}{3}\)? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, let's check the direction. Wait, if we take two points: when \(x = -6\), \(y = 0\); when \(x = 0\), \(y = 4\). So the change in \(y\) is \(4 - 0 = 4\), change in \(x\) is \(0 - (-6) = 6\), so slope is \(\frac{4}{6}=\frac{2}{3}\)? Wait, but maybe the correct points are \((0, 4)\) and \((3, 6)\): rise \(= 6 - 4 = 2\), run \(= 3 - 0 = 3\), so slope \(=\frac{2}{3}\). Wait, that makes sense. Alternatively, let's take \((-3, 2)\) and \((0, 4)\): rise \(= 4 - 2 = 2\), run \(= 0 - (-3) = 3\), so slope \(=\frac{2}{3}\). Yes, that's correct. So the slope is \(\frac{2}{3}\)? Wait, no, wait, maybe I had the rise and run reversed. Wait, slope is \(\frac{\text{rise}}{\text{run}}\), where rise is vertical change (up or down) and run is horizontal change (left or right). So if we move from \((-6, 0)\) to \((0, 4)\), we move up 4 (rise) and right 6 (run), so slope is \(\frac{4}{6}=\frac{2}{3}\).

Wait, but let's confirm with another pair. Let's take \((x_1,y_1)=(-3, 2)\) and \((x_2,y_2)=(0, 4)\). Then rise \(= 4 - 2 = 2\), run \(= 0 - (-3) = 3\), so slope \(=\frac{2}{3}\). Yes, that's correct. So the slope is \(\frac{2}{3}\).

Answer:

The slope of the line is \(\frac{2}{3}\)