Question

Describe the vertical translation between y=5x+2
and y=−7x


2 points above the equation y=−7x


y=5x+2


2 points below the equation y=−7x


−7
points below the equation y=−7x

Answer 1

There is no vertical translation that takes y = −7x to y = 5x + 2.

Reason: a vertical translation adds a constant to y and does not change the slope. Translating y = −7x vertically gives y = −7x + k for some constant k, which still has slope −7. But y = 5x + 2 has slope 5, so the slopes differ and no pure vertical shift can produce it.