What is a variable? HELP HELP
1 answer:
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Answer:
The equation that matches this situation is y = 8.34x + 25 ⇒ B
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope (rate of change)
- b is the y-intercept (initial value)
The rule of the slope is m = Δy/Δx, where
- Δy is the change of y
- Δx is the change of x
∵ Lisa collects rainwater in a barrel that weighs 25 pounds
∴ The initial value of the weight is 25 pounds
∴ b = 25
∵ When there are 10 gallons of water in the barrel, the total weight
of the barrel and the water is 108.4 pounds
∴ At x = 10, y = 108.4
∵ When there are 20 gallons of water, the total weight is 191.8 pounds
∴ At x = 20, y = 191.8
→ Find Δx and Δy
∵ Δx = 20 - 10 = 10
∵ Δy = 191.8 - 108.4 = 83.4
→ Substitute them in the rule of the slope above
∴ m =
∴ m = 8.34
→ Substitute the values of m and b in the form of the equation above
∵ y = 8.34x + 25
∴ The equation that matches this situation is y = 8.34x + 25
So the equation of the red graph is already given to us: . I assume you meant the blue graph?
We can use the vertex form: , where
is the vertex. (We can ignore
because
is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).
The vertex for is at
on the coordinate plane. (4 left, 2 down)
Plug into the vertex form:
The double negative becomes a positive, and then you're done: