Step-by-step explanation: In this problem, we are asked to graph the equation y = 2x + 3 given a domain of all real numbers.
In this situation, I would first set up a chart that we can use to organize our information. On the left side of the chart, we have our different values for x that we will be plugging into the equation. On the right side of the chart, we have our different values for y that we end up with. In the middle, we have the side of the equation that contains the x which in this case is 2x + 3.
Since our domain is all real numbers, we can choose any values we want to choose to plug into the equation for x.
Let's start with the values 1, 0, and -1 just to keep things simple. Plugging a 1 into the equation for x, we have 2 (1) + 3 or 2 + 3 which gives us 5. Plugging a zero into the equation for x, we have 2 (0) + 3 which is just 0 + 3 or 3. Plugging in -1 into the equation for x, we have 2 (-1) + 3 which is -2 + 3 or 1.
I would always choose at least 3 values to plug into the equation for x. Notice that we now have 3 points that we can use to graph this equation. Our points are (1,5), (0,3), and (-1,1). Now, we can set up our coordinate system.
Image provided of the coordinate grid and table.
Notice the pattern that is shown with these points. They all lie on the same line. In fact, if we had chosen any other value to plug into the equation for x, that point would lie somewhere on that line. The graph of this equation is the line that contains these three points.
