Question

How do you graph $y = - \dfrac{{3x}}{2} + 2$?

Answer 1

A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as $y = f(x)$, 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 answer:
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 $y = f(x)$, 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 $y = \dfrac{{ - 3x}}{2} + 2$. Let us substitute the value of x has -6, -4, -2, 0, 2, 4, and 6.
Now we consider the value of x as -6, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}( - 6) + 2 \\\ \Rightarrow y = + 9 + 2 \\\ \Rightarrow y = 11 \\\$$

Now we consider the value of x as -4, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}( - 4) + 2 \\\ \Rightarrow y = + 6 + 2 \\\ \Rightarrow y = 8 \\\$$

Now we consider the value of x as -2, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}( - 2) + 2 \\\ \Rightarrow y = + 3 + 2 \\\ \Rightarrow y = 5 \\\$$

Now we consider the value of x as 0, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}(0) + 2 \\\ \Rightarrow y = 0 + 2 \\\ \Rightarrow y = 2 \\\$$

Now we consider the value of x as 2, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}(2) + 2 \\\ \Rightarrow y = - 3 + 2 \\\ \Rightarrow y = - 1 \\\$$

Now we consider the value of x as 4, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}(4) + 2 \\\ \Rightarrow y = - 6 + 2 \\\ \Rightarrow y = - 4 \\\$$

Now we consider the value of x as 6, the value of y is

$$\Rightarrow y = \dfrac{{ - 3}}{2}(6) + 2 \\\ \Rightarrow y = - 9 + 2 \\\ \Rightarrow y = - 7 \\\$$

Now we draw a table for these values we have

X	-6	-4	-2	0	2	4	6
y	11	8	5	2	-1	-4	-7

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.