Question

# Sketch an example of a linear function in graph form.

Hint:

### The graph of a linear function is always a straight line. So we sketch a straight line in a graph and find its equation in the slope intercept form, which is y = mx + c, where m is the slope of the line and c is the y intercept.

* *

## The correct answer is: y=x

### We shall draw a straight line through the origin as shown below.

We will now derive the equation of this line in slope intercept form.

The slope intercept form is

y = mx + c

Where m is the slope and c is the y intercept.

From the graph, we can see that the line cuts the y axis at 0

So, c = 0

The slope between two points (a, b) and (c, d) is given by

We take any two points from the graph to be

(a, b) = (1,1) and (c, d) = (2, 2)

Calculating the slope, we have

Putting the value of m and c in the equation, we get

y = 1.x

That is

y = x

This is a linear equation.

This is a linear equation.

We can take any straight line in the xy plane and derive its equation in the above method; we will get a linear function. We can check this by calculating the slope between all the points. If the slope is constant everywhere, then it is linear.

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