If y = 2x + 7 were changed to y = 12x + 7, how would the graph of the new function compare with the original?
Question
If y = 2x + 7 were changed to y = 12x + 7, how would the graph of the new function compare with the original?
Solution
The graph of the new function y = 12x + 7 would be steeper than the original function y = 2x + 7. This is because the slope of the new function, which is 12, is greater than the slope of the original function, which is 2. The y-intercept of both functions is the same (7), so both graphs would cross the y-axis at the same point. However, for every unit increase in x, y increases by 12 units in the new function, compared to a 2 unit increase in the original function. This results in a steeper line for the new function.
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