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Equation of a straight line

Example 12

Find the value of the gradient and y-intercept for these relations and sketch their graphs.

Y = 2x – 1

Gradient = 2 = 2/1

Label the y intercept at (0, - 1). From the gradient 2/1 for every 1 across, move 2 up. From (0, -1) this gives a second point at (1, 1). Mark and join the points to form a line.

X + 2y = 6, rewrite in the form y = mx + c to read off the gradient and y-intercept

2y = - x + 6, make y the subject by subject by subtracting x from both sides and then dividing both sides by 2

Y = -x + 6/2, - X/2 is the same as -1/2x and 6/2 = 3

= ½ x + 3, link the negative sign to the rise (-1) so the run is positive (+2)

Mark the y-intercept at (0, 3) and then from this point move 2 right and 1 down to give a second point at (2,2)

Note that the x-intercept will be 6. If the gradient is -1/2 then a run of 6 gives a fall of three