Find the equation of the function f whose graph passes through the point and whose derivative is

Question

Find the equation of the function f whose graph passes through the point  and whose derivative is  ​

Quizplus · Accepted Answer

Let the equation of the function be f(x) = ax + b. Then, the derivative of the function is simply a. Since we are given that the derivative is equal to 11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11, we have a = 11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11. 
Now we just need to use the point (11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11, f(11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11)) = (11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11, 11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11) to solve for b: 
f(11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11) = a(11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11) + b 
11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11 = 11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11(11ea8970_6a65_cbe3_861b_fb7e150256b1_TB1301_11) + b 
b = 11ea8970_6a65_f2f6_861b_2bc731174139_TB1301_11 
Therefore, the equation of the function is f(x) = 11ea8970_6a65_cbe4_861b_8557b6ea1250_TB1301_11x + 11ea8970_6a65_f2f6_861b_2bc731174139_TB1301_11, which corresponds to choice (B).

Find the Equation of the Function F Whose Graph Passes