Question 214797
First we need to understand that the graph of an equation represents all the points whose coordinates fit the equation. In other words the ordered pair coordinates of every point on your graph must make the equation true.<br>
So we have to ask ourselves: "What ordered pairs will fit x=4?" Well it should be obvious that the x-coordinate must be a 4 in order to fit this equation. But what about the y-coordinate? There is no "y" in the equation!? What y-coordinates fit an equation which has no "y"? Answer: They ALL do!! Since there is to "y" in the equation we do not need substitute the y-coordinate into the equation to see if the ordered pair fits the equation. So as long as the x-coordinate is 4, the y-coordinate can be ANY number and the order pair still fits the equation x=4! So the solutions to x=4 are all the points with an x-coordinate of 4.<br>
And where on the coordinate plane do we find all these points with an x-coordinate of 4? With some logic or after plotting several of these points, it should become clear that these points form a vertical line 4 units to the right of the y-axis.<br>
Other clues to the graph of this type of equation are:<ol><li>The slope-intercept form of the equation of a line is: y = mx + b</li><li>Equations of the form x = [some-number] (like x=4), have no "y" and without a "y" it is <b>impossible</b> to transform the equation into slope-intercept form.</li><li>Slope is rise/run</li><li>Vertical lines have a run of 0 since they do not go sideways at all.</li><li>With a run of 0, slope is not even defined for vertical lines (since dividing by zero is undefined)</li></ol>
Fact #2 (equations of the form x = [some-number] have no slope-intercept form) and #5 (vertical lines have no defined slope) are connected. If one is true then other is also true.