Question

How do you graph the line $y = 7$ using intercepts ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as $y = f\left( x \right)$, where x and f(x) are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step by step solution:
Here in this question, we have to plot the graph for the given line using the intercepts. Intercepts of a line are the points where the straight line cuts the coordinate axes.
First, we represent the given equation in standard form of a straight line $ax + by + c = 0$. So, we get $0x + 1y - 7 = 0$.
So, to find the intercepts of the straight line given by the equation $0x + 1y - 7 = 0$, we substitute the values of x and y as zero one by one and find the value of the other variable.
So, $0x + 1y - 7 = 0$
Putting x as zero, we get,
$ \Rightarrow 0\left( 0 \right) + 1y - 7 = 0$
Simplifying the equation, we get,
$ \Rightarrow y = 7$
So, the y intercept of the straight line $y = 7$ is $\left( {0,7} \right)$.
Now, putting y as zero, we get,
$ \Rightarrow 0x + 1\left( 0 \right) - 7 = 0$
$ \Rightarrow 0x = 7$
This is not possible for any value of x. So, the straight line $y = 7$ does not cut the x axis.
Therefore, the straight line should be parallel to x-axis.
So, the graph of the line with equation $y = 7$ can be plotted as given below:

Note: The graph plotted is of two dimensional. The graph is plotted in x-axis versus y axis. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y because the value of y depends on the value of x.