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 \((0, 3)\) and \((-4, -1)\) (or other pairs, but let's use these for clarity). Wait, actually, looking at the intercepts: when \(x = 0\), \(y = 3\) (the y - intercept), and when \(y = 0\)? Wait, no, another point: let's take two clear points. Let's take \((0, 3)\) and \((4, 7)\)? Wait, no, maybe better to use the x - intercept and y - intercept. Wait, the line crosses the x - axis at \((-4, 0)\)? Wait, no, looking at the graph, the line passes through \((-4, -1)\)? Wait, maybe I made a mistake. Let's look again. The line passes through \((0, 3)\) (since when \(x = 0\), \(y = 3\)) and \((4, 7)\)? Wait, no, let's calculate the slope using two points. Let's take the point \((0, 3)\) and \((4, 7)\)? Wait, no, maybe the two points are \((-4, -1)\) and \((0, 3)\). Let's check the rise and run between these two points.

Step2: Calculate the rise

Rise is the change in \(y\) - coordinates. So if we go from \((-4, -1)\) to \((0, 3)\), the change in \(y\) is \(3-(-1)=4\).

Step3: Calculate the run

Run is the change in \(x\) - coordinates. So the change in \(x\) is \(0 - (-4)=4\).

Step4: Calculate the slope

Slope \(m=\frac{\text{rise}}{\text{run}}=\frac{4}{4} = 1\)? Wait, no, wait, maybe I picked the wrong points. Wait, let's take another pair. Let's take the point \((0, 3)\) and \((4, 7)\). Rise is \(7 - 3=4\), run is \(4 - 0 = 4\), slope is \(\frac{4}{4}=1\). Wait, or take \((-4, -1)\) and \((4, 7)\). Rise is \(7-(-1)=8\), run is \(4-(-4)=8\), slope is \(\frac{8}{8}=1\). Wait, maybe the correct two points are \((0, 3)\) and \((4, 7)\). Wait, but let's check the x - intercept. Wait, the line crosses the x - axis at \((-4, 0)\)? Wait, no, when \(y = 0\), let's solve for \(x\). If the slope is \(m\), and the y - intercept is \(b = 3\), the equation is \(y=mx + 3\). When \(y = 0\), \(0=mx+3\), \(mx=-3\). If we take a point \((x, y)\) on the line, say \((-4, -1)\), plug into \(y=mx + 3\): \(-1=m(-4)+3\), \(-4m=-4\), \(m = 1\). So the slope is \(1\).

Wait, maybe a better way: pick two points with integer coordinates. Let's take \((0, 3)\) (y - intercept) and \((4, 7)\). The rise is \(7 - 3=4\) (up 4 units), the run is \(4 - 0 = 4\) (right 4 units). Then slope \(=\frac{\text{rise}}{\text{run}}=\frac{4}{4}=1\).

Answer:

The slope of the line is \(\boldsymbol{1}\).