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A the graph of a nonconstant linear function has exactly one intersection point with the {{mvar|x}}-axis. This point is {{math|({{sfrac|−''b''|''a''}}, 0)}}. From this, it follows that a nonconstant linear function has exactly one [[zero of a function|zero]] or root. That is, there is exactly one solution to the equation {{math|1=''ax'' + ''b'' = 0}}. The zero is {{math|1=''x'' =}} {{sfrac|−''b''|''a''}}.
The points on a line have coordinates which can also be thought of as the solutions of [[linear equation]]s in two variables (the equation of the line). These solution sets define functions which are linear functions. This connection between linear equations and linear functions provides the most common way to produce linear functions.▼
== Linear function and linear equation ==
[[Image: wiki_linearna_funkcija_eks1.png|thumb||right]]<!-- are PNG and a translit from a foreign language necessary? -->
▲The points on a line have coordinates which can also be thought of as the solutions of [[linear equation]]s in two variables (the equation of the line). These solution sets define functions which are linear functions. This connection between linear equations and linear functions provides the most common way to produce linear functions.
The [[equation]] {{math|1=''y'' = ''ax'' + ''b''}} is referred to as the slope-intercept form of a [[linear equation]]. In this form, the variable is {{mvar|x}}, and {{mvar|y}}, is the value of the function. It also has two coefficients, {{mvar|a}} and {{mvar|b}}. In this instance, the fact that the values of {{mvar|y}} depend on the values of {{mvar|x}} is an expression of the functional relationship between them. To be very explicit, the linear equation is expressing the equality of values of the dependent variable {{mvar|y}} with the functional values of the linear function <math>f(x) = ax + b</math>, in other words <math>y = f(x)</math> for this particular linear function {{mvar|f}}.
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