Final answer:
Equivalent equations to y = dx + 50 have the same slope and y-intercept, indicating the same line on a graph. Operations like multiplying by a constant preserves this equivalence. Hence, an equation like 2y = 2dx + 100 is equivalent to y = dx + 50.
Step-by-step explanation:
Equations that are equivalent to y = dx + 50 must have the same structural format, meaning they represent the same line in a coordinate system. Despite various modifications, equivalent equations will have identical values for the slope and y-intercept when graphed. To create equivalent equations, one can manipulate the original equation by applying algebraic operations, such as dividing or multiplying by a constant, without changing the slope or the y-intercept.
For example, if we multiply both sides of the equation by 2, we get 2y = 2dx + 100, which is equivalent because the slope (d) and the y-intercept (50) are still effectively the same. Another operation could be adding a term and then subtracting the same term on one side, which would keep the equation unchanged in terms of its graph representation.