Question

How do you graph the line $y=6x-3$ by plotting points?

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 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 $y=f\left(x\right)$ , 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 $y=6x-3$ . Let we substitute the value of x as $0$ , $1$ , and ${\displaystyle \frac{1}{2}}$ .
Now we consider the value of x as $0$ , the value of y is
 $\Rightarrow y=6\left(0\right)-3$
 $\Rightarrow y=-3$
Now we consider the value of x as $1$ , the value of y is
 $\Rightarrow y=6\left(1\right)-3$
 $\Rightarrow y=6-3$
 $\Rightarrow y=3$
Now we consider the value of x as ${\displaystyle \frac{1}{2}}$ , the value of y is
 $\Rightarrow y=6\left({\displaystyle \frac{1}{2}}\right)-3$
 $\Rightarrow y=3-3$
 $\Rightarrow y=0$
Now we draw a table for these values we have

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.