Question

Trace the curve 3 2 y = x −1 , and state all the properties you use to trace it.

Answer 1

Given :

Equation of curve :

32y = x-1

To Find :

Tracing this curve and stating all the properties used to trace it .

Solution:

• The given equation is of a straight line, since it is of the form y = mx +c ; where m is the slope of the line and c is the intercept cut by the line on y axis
• We can also write the given equation after rearranging as  :

       $y = \frac{1}{32}.x - \frac{1}{32}$

• So, the slope of this line is $\frac{1}{32}$ which is positive , hence the line will make an acute angle with the x-axis measuring $tan^{-1}(\frac{1}{32})$.
• Also the y - intercept that it cuts is $(\frac{-1}{32})$.

Hence , the curve is shown in the attached fig .