# At a Glance - Lines

We've seen lines before. The restroom at half-time, the blue things on notebook paper...and they were all over algebra. *y = mx + b*, anyone? Lines are a special case of polynomials. Once we master them, we'll be ready to add some power. As in the power of 2. Not rangers.

Lines have a constant slope. If we write our line as *y* = *mx* + *b, *the slope will be *m*. But wait, isn't there a relationship between slope and derivative?

Yeah, they're kinda the same thing. Since lines have a constant slope the derivative of any line will just be *m*.

To recap, if *f*(*x*) = *mx *+ *b* is a line, then* f* ' (*x*) = *m*. The derivative will be constant, and equal to the slope of the line for every value of *x*.

#### Exercise 1

Find the derivative of the function *f*(*x*) = 3*x* + 5.

#### Exercise 2

Find the derivative of the function *f*(*x*) = 2*x.*

#### Exercise 3

Find the derivative of the function *f*(*x*) where *f* is the line that passes through the points (4, 5) and (-1, -2).

#### Exercise 4

Find the derivative of the function *f*(*x*) = 4.

#### Exercise 5

Find the derivative of the function *f*(*x*) = 7(*x *– 1) + 3.