You can either make a graph or write a ratio to find the slope
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The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.
<h3>What is the equation of a line passing through two points?</h3>The equation of the line passing through the points (x1, y1) and (x2, y2) is
(y - y1) = m(x - x1).
Where m is the slope of the line and is calculated by
m = (y2 - y1)/(x2 - x1)
<h3>Calculation:</h3>The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.
x: 5, 10, 15, 20, 25, 30, 35, 40
y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2
From this table, consider two points (5, 5.5) and (10, 5)
So, the equation of the line is
y- y1 = m(x - x1)
Where slope m = (y2 - y1)/(x2 - x1)
⇒ m = (5 - 5.5)/(10 - 5)
⇒ m = -0.5/5
∴ m = -0.1
Thus, the equation is
y - 5.5 = -0.1(x - 5)
⇒ y - 5.5 = -0.1x + 0.5
⇒ y = -0.1x + 0.5 + 5.5
⇒ y = -0.1x + 6.0
∴ y = -0.1x + 6
Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.
So, option 2 is correct.
Learn more about the slope of a line here:
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Answer:
see the procedure
Step-by-step explanation:
Looking at the graph we have
The graph represent a vertical parabola open upward
The vertex is a minimum
The vertex is the point (-4,-3)
The domain is the interval -----> (-∞,∞)
The Domain is all real numbers
The range is the interval ----> [-3,∞)
The range is all real numbers greater than or equal to -3
The graph is increasing in the interval (-4,∞)
The graph is decreasing in the interval (-∞,-4)
The minimum of the graph is y=-3 occurs at x=-4