Question

The equation of y=2x-1 with a translation of 3 units to the right followed by a translation of 1 unit down.

Answer 1

The equation of a line originally given by y=2x-1, after translating 3 units to the right and 1 unit down, becomes y=2x-7.

Step-by-step explanation:

The equation y=2x-1 with a translation of 3 units to the right followed by a translation of 1 unit down can be described by altering the original equation to account for these changes.

To translate a graph to the right by 3 units, we substitute (x-3) for x in the equation, resulting in y=2(x-3)-1. Then, to translate it 1 unit down, we subtract 1 from the entire equation, leading to the final transformed equation: y=2(x-3)-1-1 which simplifies to y=2x-7.

Answer 2

y = 2x - 1

Lets see something:

y = 2x - 1

y = f(x)

If we want to do translations in vertical we just have to add an constant, where postive moves it upward and negatives, downward

y = f(x) + c

y = f(x) - 1

y = 2x - 1 - 1

y = 2x - 2

Now let's see this translation to the right

If we want to translate it in horizontal we just have to add a constant inside the function, where positive moves it to the left, and negative to the right

y = f(x) - 1

y = f(x - 3) - 1

y = 2.(x - 3) - 1 - 1

y = 2x - 6 - 2

y = 2x - 8