Graphing Linear Function

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Graphing linear function involves graphing function with one and two variables. Linear functions are the functions having independent variable x never having power greater than 1. Linear function can be written in slope intercept form:f(x) = m x + b
where x and y are the co-ordinates on the graph, m is the slope of the line and b is the y- intercept. Slope shows how steep the line is.

Let us see some examples based on linear functions.

 Example 1:- Form linear function for the   graph.

Solution 1:-The linear function in the form f(x) = m x + b

From the graph it is clearly seen that y- intercept =2 so b= 2.

The slope of a line can be find by taking any 2 points on the line.

Slope of line (m) = change in y axis / change in x axis.

From the graph slope of a line = 0.5

Therefore the linear function f(x) = 0.5 x + 2 or y = 0.5 x + 2.

Example 2:-
Draw graph of linear function f(x) = y = 2x + 7

Solution2:- Assume values for x and use the function f(x) = 2 x + 7 to find values of y

When x = 1 then the value of y = 2(1) + 7 = 9

When x = -2 then the value of y = 2(-2) + 7 = 3

When x = -1 then the value of y = 2(-1) + 7 = 5

Now plot x and corresponding y values in the graph

Draw a straight line that passes through the points.

From the above examples we can clearly understood graph of linear functions.

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