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 – ExamplesOK. 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,
x = 1This 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
Correspondingly, if we next consider,
y = 1we end up with a line one notch above the x-axis!
For our final example of a line. Let’s choose, y = 2x. Some example points are,
General Equation for a LineOK. We’re ready to consider the general equation for a line. It is,
y = mx + bWe’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.
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