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Phoenix [80]
3 years ago
9

Use the graph. Which equation is true from the information in the graph?

Mathematics
1 answer:
Nikolay [14]3 years ago
7 0
From the graph, we see that two similar triangles are created by using the slope of the line.
• Because the two triangles appear to have congruent angles and proportional side lengths, we can conclude with the information we have that the two triangles are indeed similar. They are the same shape but proportional with congruent angles.
• Therefore, a/b = c/d because the scale factor remains the same of both ratios.
•We can also see that in larger triangle, the slope = 3/6 and the slope of the smaller one = 2/4. 3/6 = 2/4 because 3/6 = 1/2 and 2/4 = 1/2. Therefore, the slopes are proportional and equal.
• Because the slopes are proportional and the triangles are proportional, the a/b = c/d.
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Since it's a linear equation and there's a constant rate (given in the problem), we can choose our x - axis to be the time and the y - axis to be height. We choose it that way because you are going up in the elevator. The more time in the elevator, the higher you go.


Finding this equation uses the point slope formula, y - y₁ = m(x - x₁). It can be done with slope-intercept, y = mx + b too.).


First we need to get the slope of the line. Choose any two points, but be consistent and choose two y points as well as the matching x ones. Here, we use x₁ = 2, x₂ = 4, y₁ = 45, y₂ = 75. Slope, m, is y₂ - y₁ / x₂ - x₁.


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Next, we use the slope of 15 and either of the points to find the linear equation. Choose the same (2, 45) x-y pair above, but any point will work.


y - 45 = 15 (x - 2)

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So the linear equation representing this table us y = 15x + 15.

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