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Suppose the value of y and the value of x vary together at a constant rate of change (so that the change of Δ y = 1.25 ⋅ Δ x) and y = 2.5 when x = 3

a. We are given that y=2.5 when x=3. Plot a point on the graph to represent these values

b. Suppose the value of x varies from x=3 to x=5.25
i. By how much did the value of x change?
ii. By how much did the value of y change over this interval of x?

c. What is the value of y when x = 5.25?

Respuesta :

Intriguing456

Answer:

a) y - 2.5 = 1.25(x - 3)

b) i) Δx = 2.25

   ii) Δy = 2.8125

c) y = 5.3125

Step-by-step explanation:

We are given the proportional relationship between the rates of change of x and y:

  • Δy = 1.25 · Δx

We are also given the point:

  • x = 3
  • y = 2.5

which written as a Cartesian coordinate is:

  • (3, 2.5)

a)

We can graph this relationship by determining the slope (m), then plugging that and the given point into the point-slope form equation.

Δy = 1.25 · Δx

↓ dividing both sides by Δx

Δy / Δx = 1.25

m = Δy/Δx = 1.25

  • y - b = m(x - a)    where    (a, b) is the given point

↓ plugging into the point-slope form equation

y - 2.5 = 1.25(x - 3)

b)

i)

From x = 3 to x = 5.25, we can identify the change in x as:

Δx = 5.25 - 3

Δx = 2.25

ii)

Using the given proportional relationship, we can solve for the corresponding change in y:

Δy = 1.25 · Δx

Δy = 1.25 · 2.25

Δy = 2.8125

c)

We can find the value of y at x = 5.25 by adding the Δy we just solved for to the given y-value at x = 3:

y = 2.5 + Δy

y = 2.5 + 2.8125

y = 5.3125

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