To analyze the translation described, we start with the original point (5, 45) and see where it maps to in the new function, which is (15, 45).
The x-coordinate changes from 5 to 15, which reflects a horizontal shift of:
\[ 15 - 5 = 10 \text{ units to the right}. \]
Since the y-coordinate remains the same (both are 45), this indicates that the translation has no effect on the slope of the original function.
Therefore, the translation is best described as:
Translated horizontally 10 units to the right and has the same slope.
However, since this option isn’t explicitly available in the choices you provided, it seems there’s a slight error with options. Depending on the context, you could interpret the last option (10 units left and has the same slope) as an error in direction since the translation is actually to the right instead of the left.
If we strictly follow the options provided, the most accurate judgment based on the translation defined would be:
Translated horizontally 10 units to the right and has the same slope.