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:
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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, \( h = 9 \): \[ y = 5(x + 9) = 5x + 45 \]
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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.