By looking at the two triangles formed by the line passing through the points, we can see that they are similar triangles because they have congruent angles and proportional sides.
The first triangle has a base of 1 and a perpendicular height of 3, while the second triangle has a base of 2 and a perpendicular height of 6.
Using the similar triangles property, we can set up the proportion:
1/3 = 2/6
Cross multiplying, we get:
1 * 6 = 3 * 2
6 = 6
Therefore, the slope of the line passing through the points is 6/2 = 3.
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 four 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 3 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 3 comma 9 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 1 comma 0 right parenthesis, and left parenthesis 1 comma 3 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 3. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 1 comma 3 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.
Use similar triangles to determine the slope of the line.
(1 point)
1 answer