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Lines are an early point of investigation in calculus. This is because when you zoom in on most functions enough they look like lines. For example, you are standing on the earth and in your neighborhood it looks flat, but from outer space the surface is curved. A lot can be learned by zooming in and zooming out. A linear function is of the form $latex f(x)=mx+b&s=1$. Such a linear function gives you a line when you graph it. It takes two points to draw a line with a ruler. One point can be the y intercept which is what you get when you calculate

You can pick another point such as the x intercept or along the line at say $latex x = 1&s=1$. Find a second point then draw a line through the points with a straight edge. If the slope is known from the rise over run of two points then an equation for the line can be written in point slope form

or in standard form

The distance function between two points on our line can be found from the

Pythagorean Theorem.

The midpoint between two points on a line is found from

Another interesting property of lines is that -1/m is the slope of the line perpendicular to a line with slope m.

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