Linear Functions
One of the views of the function, f(x)=mx+b, is a straight line: any straight line on a graph. Another view is of that a linear function only has one variable and the formula for that is: f(x)=ax, where a is an integer.
Who determined the Function
Types of the Function
There are three standard forms for linear functions y = f(x):
- f(x) = mx + b (The "slope-intercept" form),
- Ax + By = C (The "general form") which defines y implicitly as a function of x as long as B=0.
- y - yo = m(x - x0) or, equivalently, f(x) = y0 + m(x - x0) (The "point-slope" or "Taylor" form)
Everyday uses of the Function
Life is full of situations when the output of a system doubles if the input doubles, and the output cuts in half if the input does the same. Some ways linear expressions are used in the real world are: measuring how long it would take to fill something, how much certain travel would cost, how much snowmelt is expected and cooking recipes.
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How to sketch it
![Picture](/uploads/3/7/1/7/37178311/5073144.jpg?250)
Often we need to know the general shape and location of a graph. In such cases, a sketch graph is drawn instead of plotting a number of points to obtain the graph.Two points are needed to obtain a straight line graph. It is simpler to find the points of intersection of the graph with the axes. These points are called the x- and y- intercepts.
What are its properties?
The exponent on a variable must be 1. M represents the gradient of the rise over run and b the increase/decrease of the y intercept. Linear functions are completely straight: in other words, they have a constant average rate of change. If the function f(x) =mx+b were to have m>0, the gradient, that is, the rise over run, would also be <0. Whereas, if the function were to be that m<0, the linear function would be decreasing from left to right. To see things more clearly, check out this interactive function.
How to graph the Function on Excel
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