Question

Write an equation of the graph in its final position.

The graph of y = 5x is translated 9 units to the left and then 4 units upward.

a. y=5 x+9 −4
b. y=5 x−9 +4
c. y=5 x−9 +4
d. y=5 x+9 +4

Answer 1

To find the equation of the graph of \( y = 5x \) after it has been translated 9 units to the left and then 4 units upward, we can follow these steps:

1. **Translation 9 units to the left**: When we translate a graph to the left by \( h \) units, we replace \( x \) with \( x + h \). In this case, \( h = 9 \):
\[
y = 5(x + 9) = 5x + 45
\]

2. **Translation 4 units upward**: When we translate a graph upward by \( k \) units, we add \( k \) to the entire function. In this case, \( k = 4 \):
\[
y = 5(x + 9) + 4 = 5x + 45 + 4 = 5x + 49
\]

The final equation of the graph after both translations is:
\[
y = 5x + 49
\]

It looks like the options provided do not contain the correct answer. It should be \( y = 5x + 49 \). None of the choices (a, b, c, d) match the final equation.