# The effect of adding b to the linear function y = ax + b

In the** previous post**, we have learned about the effects of a in the linear function with equation *y* = *a*x. In this post, we learn about the effects of adding b to that equation. That is, we want to learn the effects of *b* in the linear function with equation *y* = *ax* + *b*.

Consider the graph of the functions *y = x*, *y = x* + 2 and *y = x* – 3. The table of values (click figure to enlarge) below shows the corresponding *y* values of the three linear functions. The effect of adding 2 to the function *y = x* adds 2 to all the y values of *y = x*. This implies that in the graph, all the points with corresponding *x *values are moved 2 units above the graph of *y = x*. In addition, in the graph of *y = x* – 3, the -3 subtracts 3 from all the *y* values of *y = x*. In effect, all the points with corresponding *x* values are moved 3 units below the graph of *y = x*.

In addition, for *y = x*, if *x* = 0, *y* = 0. That means that the graph passes through the origin. On the other hand, for y = x + 2, when x = 0, then *y* = 0 + 2 = 2. This means that the graph passes through *y* = 2. Further, for y = 0 – 3 = -3. This means that the graph passes through *y* = -3. These are shown both in the table above and in the graph below.

From the observation above, we can see that the graph of the function* y = x* + *b*, passes through *y = b*. This can be easily seen because at *x* = 0, *y* = 0 + *b* which mean that *y = b*. Further, for the general linear function *y* = a*x* + *b* it has the same effect. If *x* = 0, then *y* = *a*(0) +* b = b*. Therefore, the graph of *y = ax + b*, passes through *y = b*. So, in function *y = ax + b, b* is the **y intercept** of the function.