Question

How do you graph the line $ y - 1 = 3\left( {x + 6} \right) $ ?

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 function. A graph of a function is a set of ordered pairs and it is represented as $ y = f\left( x \right) $ , where x and f(x) are real numbers. These pairs are in the form of Cartesian form and the graph is the two-dimensional graph.
First, we have to find the value of y by using the graph equation $ y - 1 = 3\left( {x + 6} \right) $ . First simplifying the equation of the line and opening the bracket, we get,
\[y - 1 = 3x + 18\]
Now, bringing the equation of the line in standard form, we get,
 $ \Rightarrow y = 3x + 19 $
Let us substitute the value of x as $ 0 $ , $ - 1 $ , $ - 2 $ , and $ - 3 $ .
Now we consider the value of x as $ 0 $ , the value of y is
 $ \Rightarrow y = 3\left( 0 \right) + 19 $
 $ \Rightarrow y = 19 $
Now we consider the value of x as $ - 1 $ , the value of y is
 $ \Rightarrow y = 3\left( { - 1} \right) + 19 $
 $ \Rightarrow y = 16 $
Now we consider the value of x as $ - 2 $ , the value of y is
 $ \Rightarrow y = 3\left( { - 2} \right) + 19 $
 $ \Rightarrow y = 13 $
Now we consider the value of x as $ - 3 $ , the value of y is
 $ \Rightarrow y = 3\left( { - 3} \right) + 19 $
 $ \Rightarrow y = 10 $
Now we draw a table for these values we have,

x	$ 0 $	$ - 1 $	$ - 2 $	$ - 3 $	$ - 6 $
y	$ 19 $	$ 16 $	$ 13 $	$ 10 $	$ 1 $

The graph plotted for this point is represented below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. 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. Hence, we have plotted the graph.