Straight line graphs The graph of each of these equations is a straight line: If an equation can be rearranged into the form , then its graph will be a straight line. In the above: can be rearranged as (which can be re-written as can be rearranged as ). . can be rearranged as or . Vertical and horizontal lines Vertical lines have equations of the form Horizontal lines have equations of the form . . Example Draw the graph of . Mark some points on a grid which have an -coordinate of 3, such as (3, 0), (3, 1), (3, -2). The points lie on the vertical line Lines in the form where and . are vertical and lines in the form are numbers. are horizontal, Plotting straight line graphs A table of values can be used to plot straight line graphs. Example Draw the graph of Create a table of values: x . -1 0 y 1 2 3 2 5 8 Plotting the coordinates and drawing a line through them gives: This is the graph of . Sketching straight line graphs If you recognise that the equation is that of a straight line graph, then it is not actually necessary to create a table of values. Just two points are needed to draw a straight line graph, although it is a good idea to do a check with another point once you have drawn the graph. Example Draw the graph of . If you recognise this as a straight line then just choose two ‘easy’ values of , work out the corresponding values of and plot those points. When , . Plot (0, −1). When , . Plot (2, 5). Drawing the line through (0. -1) and (2, 5) gives the line above. Example Draw the graph of . If you recognise this as a straight line then: When , then means , so . Plot (0, 4). When , then means , so . Plot (6, 0). Draw the line through (0, 4) and (6, 0). Now check: The drawn graph passes through (3, 2). Does (3, 2) satisfy does equal 12, so we can be confident that our line is correct.