Question

What is the answer of question 17 in lesson 2.1 translations

Answer 1

9514 1404 393

Answer:

• y = 2x
• (1, 2)

Step-by-step explanation:

The line representing Murphy street goes through point (0, 3) and has a slope of 2/1 = 2. Its equation is then ...

  y = mx + b

  y = 2x +3

The translation vector transforms this equation* by adding -1 to y, and replacing x with x-1.

  y = (2(x-1)) +3) -1

  y = 2x -2 +3 -1 . . . . eliminate parentheses

  y = 2x . . . . . . . . . . . the equation for Nolan street

__

Of course, adding (1, -1) to the point (0, 3) moves it to ...

  (1, -1) +(0, 3) = (0+1, -1+3) = (1, 2)

The image of (0, 3) is (1, 2).

_____

* f(x) is translated by (a, b) this way: g(x) = f(x-a) +b. Here, f(x) = 2x+3 is translated to f(x-1)+(-1) = (2(x-1) +3) -1.