Question
Find the slope of the given line using similar triangles.
1/4
-4
4
−14
1/4
-4
4
−14
Answers
GPT 3.5
To find the slope of a line using similar triangles, we can use the fact that the slope of a line is the ratio of the vertical distance to the horizontal distance between two points on the line.
For the first line with a slope of 1/4, let's consider two points on the line, (0, 0) and (4, 1). The vertical distance between these two points is 1 and the horizontal distance is 4. The ratio of the vertical distance to the horizontal distance is 1/4, so the slope of the line is 1/4.
For the second line with a slope of -4, let's consider two points on the line, (0, 0) and (2, 8). The vertical distance between these two points is 8 and the horizontal distance is 2. The ratio of the vertical distance to the horizontal distance is 8/2, which simplifies to 4. However, since the slope is negative, the slope of the line is -4.
For the third line with a slope of 4, let's consider two points on the line, (0, 0) and (1, 4). The vertical distance between these two points is 4 and the horizontal distance is 1. The ratio of the vertical distance to the horizontal distance is 4/1, which simplifies to 4. Therefore, the slope of the line is 4.
For the fourth line with a slope of -14, let's consider two points on the line, (0, 0) and (1, -14). The vertical distance between these two points is -14 (since it is going downwards) and the horizontal distance is 1. The ratio of the vertical distance to the horizontal distance is -14/1, which simplifies to -14. Therefore, the slope of the line is -14.
For the first line with a slope of 1/4, let's consider two points on the line, (0, 0) and (4, 1). The vertical distance between these two points is 1 and the horizontal distance is 4. The ratio of the vertical distance to the horizontal distance is 1/4, so the slope of the line is 1/4.
For the second line with a slope of -4, let's consider two points on the line, (0, 0) and (2, 8). The vertical distance between these two points is 8 and the horizontal distance is 2. The ratio of the vertical distance to the horizontal distance is 8/2, which simplifies to 4. However, since the slope is negative, the slope of the line is -4.
For the third line with a slope of 4, let's consider two points on the line, (0, 0) and (1, 4). The vertical distance between these two points is 4 and the horizontal distance is 1. The ratio of the vertical distance to the horizontal distance is 4/1, which simplifies to 4. Therefore, the slope of the line is 4.
For the fourth line with a slope of -14, let's consider two points on the line, (0, 0) and (1, -14). The vertical distance between these two points is -14 (since it is going downwards) and the horizontal distance is 1. The ratio of the vertical distance to the horizontal distance is -14/1, which simplifies to -14. Therefore, the slope of the line is -14.