How do you graph the equation #y=8x# by making a table and what is its domain and range?

Question

Nathan Axel · Accepted Answer

Build the table with any convenient values for x that you want. Find corresponding values for y and transfer to the graph. Both domain and range are all real number from -#oo# to +#oo#

As stated, make two columns in the table, x and y. Now, choose simple values for x, like 1, 2, 3, 4. Use the equation to find corresponding values of y: 8, 16, 24 and 32 in this case. Now, draw the graph - making sure the y-axis can handle the large values! Plot the four points on the graph. You should find that the four points lie in the same line. Draw the line that passes through them, extending it beyond the values you plotted. Use arrows to show that the line can extend in both directions.

Since any value from -#oo# to +#oo# could be a valid choice for x, the domain (set of all possible x-values) is -#oo# to +#oo#.

Likewise, there is no value of y that could not appear on your graph, so the range (set of possible y-values) is also -#oo# to +#oo#.

Hazel Anglin · Answer

undefined To graph the equation $y = 8x$ using a table, you can choose a set of x-values, plug them into the equation to find the corresponding y-values, and then plot the points on a coordinate plane.

Let's choose some x-values: -2, -1, 0, 1, and 2.

When $x = -2$, $y = 8(-2) = -16$.  
When $x = -1$, $y = 8(-1) = -8$.  
When $x = 0$, $y = 8(0) = 0$.  
When $x = 1$, $y = 8(1) = 8$.  
When $x = 2$, $y = 8(2) = 16$.

So, the table of values is:

|   x   |   y   |
|-------|-------|
|  -2   |  -16  |
|  -1   |  -8   |
|   0   |   0   |
|   1   |   8   |
|   2   |   16  |

The domain of the function $y = 8x$ is all real numbers because there are no restrictions on the values of $x$.

The range of the function $y = 8x$ is also all real numbers because as $x$ varies, $y$ varies proportionally and can take on any real value.

To graph the equation, plot the points from the table on a coordinate plane and draw a straight line passing through them.

It's important to note that the graph of $y = 8x$ is a straight line passing through the origin (0,0) with a slope of 8.