Question

How do you graph \[y = - \dfrac{1}{2}\] using intercepts?

Answer 1

Hint: Linear equations in the form \[y = a\] have no \[x\]-intercept. The linear equation \[y = a\] is a line parallel to \[x\]-axis that intercept \[y\]-axis at point \[\left( {0,a} \right)\]. Therefore, the graph is a line parallel to the x-axis that cuts the y-axis at negative of half for the given equation.

Complete step-by-step solution:
The given equation \[y = - \dfrac{1}{2}\] can be written as shown below.
\[ \Rightarrow y = - \dfrac{1}{2} + 0x\] …… (1)
We are asked to draw the graph using the intercepts.
It is observed that a given equation is one of the equations of a straight line. We know this fact because both x and y terms in the equation are of power 1 (so they are not squared or square rooted terms).
We can simplify the given equation, so that our calculation becomes easier.
We find the points of intercepts and then draw a line through them as at least two points are needed to draw a unique line.
Finding the \[x\]-intercept:
The line crosses the x-axis at \[y = 0\].
Taking \[y = 0\] in the equation (1) we get,
\[ \Rightarrow 0 = - \dfrac{1}{2} + 0x\]
This can be written as,
\[ \Rightarrow 0 = - \dfrac{1}{2}\]
This is a false equation. It implies that our substitution \[y = 0\] is not true.
This further implies that the line of a given equation does not have a \[x\]-intercept, in other word line is parallel to \[x\]-axis.
Finding the \[y\]-intercept:
The line crosses the y-axis at \[x = 0\].
Taking \[x = 0\] in the equation (1) we get,
\[ \Rightarrow y = - \dfrac{1}{2} + 0\left( 0 \right)\]
This can be written as,
\[ \Rightarrow y = - \dfrac{1}{2}\]
So the point is \[\left( {0, - \dfrac{1}{2}} \right)\].
Hence the line does not have \[x\]-intercept and the \[y\]-intercept is \[\left( {0, - \dfrac{1}{2}} \right)\].
Now, we plot the graph on the x-y plane such that it cuts the y –axis at \[ - \dfrac{1}{2}\] and parallel to x-axis as shown in the below figure.

Note that the graph is a straight line parallel to x-axis.

Note: Students must remember that to obtain the \[x\]-intercept, we set the value of y equal to zero and find the point. Then, to obtain the \[y\]-intercept, we set the value of x equal to zero and find the point. Then from obtained \[(x,y)\] points we plot a graph of the given equation in the x-y plane.