Maths-
General
Easy

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
    m equals fraction numerator d minus b over denominator c minus a end fraction
    We take any two points from the graph to be
    (a, b) = (1,1) and (c, d) = (2, 2)
    Calculating the slope, we have
    m equals fraction numerator 2 minus 1 over denominator 2 minus 1 end fraction equals 1 over 1 equals 1
    Putting the value of m and c in the equation, we get

                                      y = 1.x

    That is

                                       y = x
    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.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.