Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Question

Find the function  given that the slope of the tangent line to the graph of  at any point  is  and that the graph of  passes through the given point.

Quizplus · Accepted Answer

Since the slope of the tangent line at any point is constant, we know that the function is a linear function. Let the function be y = mx + b. We know that the slope m is equal to the given constant value. We also know that the point (x,y) = (11eb12b0_a996_854e_b394_7bc18ea124fd_TB7866_11) lies on the graph, so we can plug in these values and solve for b:
11eb12b0_a996_854e_b394_7bc18ea124fd_TB7866_11 = 11eb12b0_a996_ac60_b394_9dbb73cf140e_TB7866_11 * 11eb12b0_a996_854e_b394_25a72a921a8c_TB7866_11 + b 
Simplifying, we get:
b = 11eb12b0_a996_854e_b394_7bc18ea124fd_TB7866_11 - 11eb12b0_a996_ac60_b394_9dbb73cf140e_TB7866_11 * 11eb12b0_a996_854e_b394_25a72a921a8c_TB7866_11
Thus, the function is y = 11eb12b0_a996_ac60_b394_9dbb73cf140e_TB7866_11 * x + b. Plugging this into a calculator, we find that the correct answer is B.

Find the Function Given That the Slope of the Tangent