Suppose the value of y and the value of x vary together at a constant rate of change (so that Δy = 0.75. Δx), and y = 1.5 when x = 3. a. What is the constant rate of change of y with respect to x? b. Write a formula that expresses y in terms of x. c. What is the value of y when x=103?

a. 0.75

b. y = 0.75 x - 0.75

c. 76.5

Step-by-step explanation:

a. What is the constant rate of change of y with respect to x?

We know that the value of y and the value of x vary together at a constant rate of change so that Δy = 0.75. Δx. Then, the rate of change is:

Δy / Δy = 0.75

b. Write a formula that expresses y in terms of x.

The formula of the linear expression that relates x and y is:

y = 0.75 x + b

where,

0.75 y the slope

b is the intercept

We know that when x = 3, y = 1.5. Then,

1.5 = 0.75. 3 + b

b = - 0.75

The resulting formula is

y = 0.75 x - 0.75

c. What is the value of y when x = 103?

When x = 103

y = 0.75. 103 - 0.75

y = 76.5