Along the horizontal x-axis, starting to the right of the (0, 0) point, write little numbers like a ruler has, 1, 2, 3, and so forth. To the left of that point, write, -1, -2, -3, and so on. For the y-axis, the 1, 2, 3, and such go upward, whereas the -1, -2, -3 and the rest go downwards.

## Equation of a Line – Examples

OK. We’ve prepared our coordinate system. Using it as a kind of mapping aid, we will draw the simplest of equations, that of a straight line. What does the general equation for a line look like? Before we discuss that, we’ll first consider three examples. First, the line,**This equation means that no matter what value y has, x has the value one. Let’s draw some points to demonstrate what we mean. We’ll pick y = 0, y = 2, y = 5, y = -3. Then, we get**

x = 1

**Locating these on our coordinate axes, we see that all we are doing is drawing a line parallel to the y-axis, but to the right one notch!**

(1, 0)

(1, 2)

(1, 5)

(1, -3)

Correspondingly, if we next consider,

**we end up with a line one notch above the x-axis!**

y = 1

For our final example of a line. Let’s choose, y = 2x. Some example points are,

(0, 0)

(1, 2)

(3, 6)

(-2, -4)

(-2.5, 5)

## General Equation for a Line

OK. We’re ready to consider the general equation for a line. It is,**We’ve already seen that m is a number representing the slope of the line. What, then, is b? It determines where the line crosses the y-axis. To demonstrate that, choose x = 0. Then if b = 2.7, for instance, y = 2.7. The line crosses the y-axis at (0, 2.7). This is the reason why b is called the “intercept.” It represents the point where the line intercepts the y-axis.**

y = mx + b

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