Answer:
Explanation:
Here's a graph of a line with a negative slope:
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The line descends from left to right.
To draw the slope triangles, we can choose any two points on the line and draw a triangle with one vertex at each point. Let's choose the points (0, 4) and (3, 0):
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T2
The height of the first triangle, T1, is the difference between the y-coordinates of the two points: 4 - 0 = 4. The base of T1 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T1 is 4/3.
The height of the second triangle, T2, is the difference between the y-coordinates of the two points: 0 - 4 = -4. Note that because the slope of the line is negative, the height of the triangle is negative as well. The base of T2 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T2 is (-4)/3, which simplifies to -1.33.
The slope of the line is defined as rise divided by run. In this case, the rise is -4 (because the line is descending) and the run is 3. So the slope is (-4)/3, which is approximately -1.33. We can see that the simplified ratio of the rise/run of each triangle is indeed equivalent to the slope of the line.