Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = −6 and g'(2) = 4.

Question

Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = −6 and g'(2) = 4.

 (Enter your answer as an equation in terms of y and x.)

Answer 1

You are writing an equation of a line, so use the point slope formula y-y₁=m(x-x₁).

To fill in the formula, you will need a point and a slope (derivative).

Your point is (2,-6)

Your slope (derivative) at 2 is 4.

Your answer: y- -6=4(x-2).

Note that the double negative can be written as a positive and your answer can be put into y=mx+b form.