Question

A linear function, () passes through the points (2, 8) and (5, 17). The function was replaced with ( + ) resulting in the function (). The function () passes through the points (2, 14) and (5, 23). W hat is the value of ?

Answer 1

We can find the original function using the formula

`(x-x_2)/(x_1-x_2)=(y-y_2)/(y_1-y_2)`

Plugging your values, we have

`(x-5)/(2-5)=(y-17)/(8-17) \iff (x-5)/(-3)=(y-17)/(-9)\iff (x-5)/(3)=(y-17)/(9)`

Multiply both sides by 9 to get

`y-17=3x-15 \iff y=3x+2`

So, the transformed function is

`y=3(x+k)+2=3x+(2+3k)`

Impose the passing through (2, 14) to get

`14=3\cdot 2+(2+3k) \iff 14=6+2+3k \iff 3k=6 \iff k=2`

So, the new function is

`y=3x+8`