Find an equation of the tangent line to the graph of
y = g(x) at x = 5 if g(5) = −3 and g'(5) = 6
+9466 g'(5) = 6
This means the slope of the tangent line we're after is 6.
g(5) = -3
This means the tangent line passes through the point (5,-3).
So now all we need to do is simply find the equation for a line with a slope of 6 that passes through the point (5,-3).
y = mx + b
Plug in what we know and solve for what we don't (in this case, b).
-3 = 6(5) + b
-3 = 30 + b
-33 = b
Now use the slope and y intercept to make the equation.
y = 6x - 33
