Question

30 POINTS PLS HELP

The slope of the linear function y= 5/4x +1/2 is changed to 5/8 where y= 5/8x + 1/2. Identify the transformation required to produce the new slope, state the equation of the transformed function, ande explainw hat the graph of the tranfsformed line look like.
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Answer 1

We proceed to use the following operations: (i) Vertical translation downwards (
`k = -(1)/(2)`), (ii) Vertical compression (
`c = (1)/(2)`), (iii) Vertical translation upwards (
`k = (1)/(2)`). The graph is presented below.

Explanation:

To transform
`y = (5)/(4)\cdot x + (1)/(2)` into
`y = (5)/(8)\cdot x + (1)/(2)`, we apply the following steps:

(i) Vertical translation downwards (
`k = -(1)/(2)`)

`g(x) = f(x) +k` (1)

(ii) Vertical compression (
`c = (1)/(2)`)

`g(x) = c\cdot f(x)` (2)

(iii) Vertical translation upwards (
`k = (1)/(2)`)

`g(x) = f(x) + k`

Now, we proceed to transform the primitive expression:

Step 1

`f'(x) = (5)/(4)\cdot x`

Step 2

`f''(x) = (5)/(8)\cdot x`

Step 3

`g(x) = (5)/(8)\cdot x + (1)/(2)`

The graph of both function are now presented below. The parent function is the red line and the new function is represented by the blue line.