(a)Show that the lines y=3x+7 and 2y–6x=8 are parallel. [3 marks] (b) Is the point (–5, –6) above, below or on the line y = 3x + 7 ? Do not use a graphical method. [2 marks] [Total 5 marks]
(a) The gradient of y=3x+7 is 3 and rearrange 2y–6x=8 to y=3x+4 to show the gradient of 2y–6x=8 is also(6÷2=) 3. Alternatively, choose a value for x and find y value for both lines (e.g. (0, 7) and (0, 4)); then choose a different value for x and find y value for both lines again (e.g. (1, 10) and (1, 7)); state that the y values are a constant distance apart so they are parallel lines.(b)Substitute -5 in the equation e.g. 3 × –5 + 7 = –8 to get the point (–5, –8). Using y co-ordinates -6 is higher than -8 so (-5,-6) is above the line.
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