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:

To determine the slope of the line, we first identify two points on the line. From the graph, we can see that the line passes through the origin \((0, 0)\) and another point, say \((8, -2)\) (we can verify this by looking at the grid).

Step 1: Recall the formula for slope

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m=\frac{y_2 - y_1}{x_2 - x_1}
\]

Step 2: Identify the coordinates of two points

Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(8, - 2)\)

Step 3: Calculate the rise and run

The "rise" is the change in \(y\)-values, \(y_2-y_1=-2 - 0=-2\)
The "run" is the change in \(x\)-values, \(x_2 - x_1=8-0 = 8\)

Step 4: Calculate the slope

Using the slope formula:
\[
m=\frac{-2}{8}=\frac{-1}{4}
\]

The slope of the line is \(\boxed{-\dfrac{1}{4}}\)

(Note: For drawing the "rise" and "run", we start from the point \((0,0)\), draw a vertical line (rise) down 2 units (since the rise is - 2) to the point \((0,-2)\) and then a horizontal line (run) to the right 8 units to the point \((8,-2)\), or we can use the two points \((0,0)\) and \((8, - 2)\) to draw the rise and run. The rise is the vertical segment between the two points and the run is the horizontal segment between the two points.)

Answer:

To determine the slope of the line, we first identify two points on the line. From the graph, we can see that the line passes through the origin \((0, 0)\) and another point, say \((8, -2)\) (we can verify this by looking at the grid).

Step 1: Recall the formula for slope

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m=\frac{y_2 - y_1}{x_2 - x_1}
\]

Step 2: Identify the coordinates of two points

Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(8, - 2)\)

Step 3: Calculate the rise and run

The "rise" is the change in \(y\)-values, \(y_2-y_1=-2 - 0=-2\)
The "run" is the change in \(x\)-values, \(x_2 - x_1=8-0 = 8\)

Step 4: Calculate the slope

Using the slope formula:
\[
m=\frac{-2}{8}=\frac{-1}{4}
\]

The slope of the line is \(\boxed{-\dfrac{1}{4}}\)

(Note: For drawing the "rise" and "run", we start from the point \((0,0)\), draw a vertical line (rise) down 2 units (since the rise is - 2) to the point \((0,-2)\) and then a horizontal line (run) to the right 8 units to the point \((8,-2)\), or we can use the two points \((0,0)\) and \((8, - 2)\) to draw the rise and run. The rise is the vertical segment between the two points and the run is the horizontal segment between the two points.)