Question

How do you find the equation of a line tangent to `y=4-3x` at (1,1)?

Answer 1

See below.

Explanation:

The first derivative of `f(x)=4-3x` allows us to find the gradient of the tangent line to any point on `f(x)=4-3x`.

If we look at the function `f(x)=4-3x`, we notice that this is the equation of a line. The gradient of a line is constant, in this case `-3`. The tangent line to any point is the line itself.

i.e.

`y=4-3x`

Therefore there is nothing to find here.