Question

How do you find the slope and intercept of $2{\text{y - 1 = 0}}$ ?

Answer 1

Hint: In this question we are given with a line whose equation is $2{\text{y - 1 = 0}}$ and are asked to find out its slope and its intercept. We can find the slope and intercept of the given equation $2{\text{y - 1 = 0}}$ by substituting the values in the given formula. On simplification we get the required answer.

Formula used: For any equation \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] ,
Slope (m) = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
To find intercept,
 \[{\text{y - intercept}} = \dfrac{{ - {\text{C}}}}{{\text{B}}}\]

Complete step-by-step solution:
First we have to find the slope of the given equation $2{\text{y - 1 = 0}}$, for any equation \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\], the formula for slope is given by:
Slope (m) = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
For this we have to compare the given equation $2{\text{y - 1 = 0}}$ and \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\]
Then change it into the form of \[{\text{Ax}} + {\text{ By }} + \;{\text{C}}\; = \;0\] to find the values of ${\text{A,B and C}}$.
That is, $0{\text{x + }}2{\text{y - 1 = 0}}$
So here we get,
 ${\text{Ax = 0}}$
${\text{By = 2y}}$
${\text{C = - 1}}$
So the Slope (m) of the line = $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
Therefore slope of $2{\text{y - 1 = 0}}$is $\dfrac{{ - {\text{A}}}}{{\text{B}}}$
$ \Rightarrow - \dfrac{0}{{2{\text{y}}}}$
${\text{slope (m) = 0}}$
Now, to find the intercept of$2{\text{y - 1 = 0}}$, we have to use the formula of y-intercept,
\[{\text{y - intercept}} = \dfrac{{ - {\text{C}}}}{{\text{B}}}\]
As we know,
${\text{Ax = 0}}$
${\text{By = 2y}}$
${\text{C = - 1}}$
${\text{m = 0}}$
Therefore by using the formula we get,
\[{\text{y - intercept}} = \dfrac{{ - {\text{C}}}}{{\text{B}}}\]
\[{\text{y - intercept}} = \dfrac{{ - ( - 1)}}{2}\]
\[{\text{y - intercept}} = \dfrac{1}{2}\]

Hence the slope and y- intercept of the given equation $2{\text{y - 1 = 0}}$ is slope (m)${\text{ = 0}}$ and y- intercept \[ = \dfrac{1}{2}\]

Note: In this question we have to alternative method as follows:
This is an alternative method to find the y-intercept,
The equation of slope intercept form is ${\text{y = mx + b}}$,where ${\text{m}}$ is the slope of the line and ${\text{b}}$ is the y-intercept.
Now the equation is $2{\text{y - 1 = 0}}$, we have to change this in the form of ${\text{y = mx + b}}$
$ \Rightarrow 2{\text{y - 1 = 0}}$
Transferring numbers to one side, we get
$ \Rightarrow 2{\text{y = 0 + 1}}$
Now dividing $2$ on both the sides we get,
$ \Rightarrow {\text{y = }}\dfrac{{\text{1}}}{2}$
$ \Rightarrow {\text{y = 0(x) + }}\dfrac{1}{2}$, which is now in the form of ${\text{y = mx + b}}$
Therefore the intercept of the given equation $2{\text{y - 1 = 0}}$ is y- intercept =\[{\text{b}} = \dfrac{1}{2}\].