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An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through five plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 1 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma 0 right parenthesis, and left parenthesis 4 comma 2 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 4 comma 2 right parenthesis, left parenthesis 8 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2.

Use similar triangles to determine the slope of the line. Write your answer in fraction form.

(1 point)
The slope is
.
Remaining Attempts : 3
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1 answer

To determine the slope of the line using the given points, we can use the slope formula, which is defined as:

\[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} \]

From the given points, we know two coordinates through which the line passes:

  1. (0, 0)
  2. (2, 1)
  3. (4, 2)
  4. (6, 3)
  5. (8, 4)

Let's calculate the slope using the first and last points:

  • The change in \( y \) from (0, 0) to (8, 4): \[ \Delta y = 4 - 0 = 4 \]

  • The change in \( x \) from (0, 0) to (8, 4): \[ \Delta x = 8 - 0 = 8 \]

Now we can substitute these values into the slope formula:

\[ \text{slope} = \frac{4}{8} = \frac{1}{2} \]

Thus, the slope of the line is:

\[ \boxed{\frac{1}{2}} \]