Question

How do you write \[y=\dfrac{1}{2}x-1\] in standard form?

Answer 1

Hint: Multiply both the sides with 2 and simplify the given equation of straight line. Now, take all the terms to the L.H.S. and write the simplified equation in the form: - \[ax+by+c'=0\] to get the answer, i.e., the equation of a line in standard form. Here, ‘a’ is the coefficient of x, ‘b’ is the coefficient of y and ‘c’ is the constant term.

Complete step-by-step solution:
Here, we have been provided with the equation of line \[y=\dfrac{1}{2}x-1\] and we are asked to convert it into the standard form. But first we need to know about the given form and the standard form of a straight line.
Now, here we have the equation \[y=\dfrac{1}{2}x-1\] which is similar to the equation \[y=mx+c\]. This form of straight line is known as the slope – intercept form, where ‘m’ is the slope and ‘c’ is the intercept on y – axis. Now, the standard form of a straight line is given as: - \[ax+by+c'=0\], where ‘a’ is the coefficient of x, ‘b’ is the coefficient of y and c’ is the constant term. So, let us write the given equation of line in standard form. We have,
\[\because y=\dfrac{1}{2}x-1\]
Multiplying both the sides with 2, we get,
\[\Rightarrow 2y=x-1\]
Taking all the terms to the L.H.S., we get,
\[\begin{align}
  & \Rightarrow 2y-x+1=0 \\
 & \Rightarrow -x+2y+1=0 \\
\end{align}\]
On comparing the above equation \[ax+by+c'=0\], we have,
\[\Rightarrow \] a = -1, b = 2, c’ = 1
Hence, \[-x+2y+1=0\] is the required standard form of the equation.

Note: One may note that here we have multiplied the given equation with 2 at the initial stage of the solution because generally we try to get rid of fractional terms while writing the standard form of a straight line. You must remember all the forms and their general equations for a straight line, like: - intercept form, slope – intercept form, point slope form, standard form, polar form, parametric form etc. Remember that these forms are easily interconvertible.