Use the image to answer the 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 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.
The two triangles formed are similar, as they have equal angles and proportional sides. Therefore, we can set up a proportion using the base and height of each triangle.
For the first triangle:
Base/Height = 4/2
For the second triangle:
Base/Height = 4/2
Simplifying both proportions, we get:
2/1 = 4/Slope
2Slope = 4
Slope = 4/2
Slope = 2
Therefore, the slope of the line is 2.
That's wrong
Let's use the points on the line to determine the slope using the formula:
Slope = (change in y) / (change in x)
Let's take two points on the line: (0,0) and (2,1)
(change in y) = 1 - 0 = 1
(change in x) = 2 - 0 = 2
Slope = 1/2
Therefore, the slope of the line is 1/2.