Question

Compute delta y/delta x for the interval [2,5], where y = 4x - 9.

Answer 1

The delta y/delta x for the interval [2,5] is 4.

Step-by-step explanation:

To compute delta y/delta x for the interval [2,5], we need to find the change in y divided by the change in x between the two endpoints of the interval. The given equation is y = 4x - 9.

Let's calculate the values of y at x = 2 and x = 5:
For x = 2: y = 4(2) - 9 = -1.
For x = 5: y = 4(5) - 9 = 11.

The change in y is 11 - (-1) = 12, and the change in x is 5 - 2 = 3. Therefore, the delta y/delta x for the interval [2,5] is 12/3 = 4.

Answer 2

We have to compute: Δ y / Δ x.
The interval is [ 2, 5 ] and y = 4 x - 9.
y 1 = 4 · 2 - 9 = 8 - 9 = - 1
y 2 = 4 · 5 - 9 = 20 - 9 = 11
Δ y / Δ x = ( y 2 - y 1 ) / ( x 2 - x 1 ) =
= ( 11 - ( - 1 ) ) / ( 5 - 2 ) = ( 11 + 1 ) / 3 = 12 / 3 = 4
Answer:
Δ y / Δ x = 4