Question

Can you write a rule for finding the output (absolute guessing error) given the input (a guess)?

Answer 1

The rule for the plotted line is
`y = \left | x - 50 \right |`

Explanation:

The coordinates when y = 0, x = 50

When y = 10, x = 60

Therefore, the slope = (10 - 0)/(60 - 50) = 1

The equation in slope and intercept form is y - 10 = 1 × (x - 60)

y = x -60 + 10 = x -50

y = x - 50

Also, we have

When y = 20, x = 30

y = 10, x = 40

Therefore, the slope = (10 - 20)/(40 - 30) = -1

The equation in slope and intercept form is y - 10 = -1 × (x - 40)

y = -x + 40 + 10

y = 50 - x

Therefore, when x < 50, y = 50 - x

When x > 50, y = x - 50

Which is equivalent to
`y = \left | x - 50 \right |`

The rule for the plotted line is
`y = \left | x - 50 \right |`