Step-by-step explanation:
basic line function
y = 6x + 3
a translation (= a shift) upward by 5 simply means that all y values are incremented by 5 compared to the original results.
so, the function is then
y = 6x + 3 + 5 = 6x + 8
now we reflect this across the y-axis (mirror it left/right).
the simply means the slope flips its sign (+ to -, or - to +).
the slope is the factor of x (6).
but everything else stays the same (the same y-intercept, as the y-axis is the "mirror").
so, we get a final result
y = -6x + 8
and now the other way around :
first we reflect axis the y-axis leading to (same arguments as with the previous reflection)
y = -6x + 3
and then we translate this upward by 5 units leading to
y = -6x + 3 + 5 = -6x + 8
so, both final results are the same.
