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Question

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 1 comma 2 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 6 right parenthesis, and left parenthesis 4 comma 8 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 3 comma 0 right parenthesis, and left parenthesis 3 comma 6 right parenthesis. The base is labeled as 3, and the perpendicular height on the right is labeled as 6. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 3 comma 6 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 2.

Use similar triangles to determine the slope of the line.

(1 point)
The slope is
Remaining Attempts : 3
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Answer 1

To determine the slope of the line using the given points, we apply the formula for the slope, which is defined as the rise over the run. We have several points through which the line passes:

• (0, 0)
• (1, 2)
• (2, 4)
• (3, 6)
• (4, 8)

We can see that as we move from the point (0, 0) to (1, 2), the rise (change in y) is 2 - 0 = 2, and the run (change in x) is 1 - 0 = 1.

The slope \( m \) can be calculated as:

\[ m = \frac{\text{rise}}{\text{run}} = \frac{2}{1} = 2. \]

To confirm this with the larger triangle formed at points (0, 0), (3, 0), and (3, 6):

• The rise from (0, 0) to (3, 6) is 6.
• The run from (0, 0) to (3, 0) is 3.

Calculating the slope using these points gives us:

\[ m = \frac{6}{3} = 2. \]

Therefore, the slope of the line is:

2.