Why is the addition or subtraction of k to the output of a function considered a translation?

Match the equivalent expressions. x - 3y + 12 12 - 3y - 2x + x + 2x 3x + 2y - 2x + y + 12 3y + 12 3x + y - 12 4y + 3y + 3x - 6y - 10 - 2 x + 3y + 2x - 3x + 7 + 5 x + 3y + 12 5 + 2y + 7x - 4x + 3y - 17

What is the y-intercept of the line given by the equation

Pls what is the relative minimum of the function? enter your answer in the box