1 Consider the graph of \( y=4 x+1 \). What is the equation of the graph after it has been translated 2 units to the right? A. \( y=2 x-7 \) B. \( y=2 x+9 \) C. \( y=4 x-7 \) D. \( y=4 x+9 \)

When we translate a function to the right by a certain number of units, we replace \( x \) in the equation with \( x-h \), where \( h \) is the number of units translated. In this case, for a 2-unit translation to the right, our original equation \( y = 4x + 1 \) becomes \( y = 4(x - 2) + 1 \). Simplifying this, we get \( y = 4x - 8 + 1 = 4x - 7 \). Therefore, the correct answer is C. \( y = 4x - 7 \). Now, how cool is it to watch a simple equation transform with a little bit of movement? Just like how we move around in our own lives, equations can shift and change in a similar way! It's a fun reminder that math isn’t just numbers; it’s all about transformations and relationships! To bolster your understanding of these transformations, you might want to explore the basics of function translations in algebra. Often, people forget that moving functions around is as simple as plugging in different values for \( x \). Maintaining a fun attitude toward learning can make grasping these concepts much easier!