How do you find the slope of $y = 2 | x - 3 | + 5$ $y=2|x-3|+5$ ?

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How do you find the slope of $y = 2 | x - 3 | + 5$ $y=2|x-3|+5$ ?

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Answer 1 · 2016-10-03T11:27:22

This one has two slopes

Explanation:

If $x \geq 3$ $x>=3$ then the slope is $+ 2$ $+2$ because the function is equivalent to
$y = 2 (x - 3) + 5 = 2 x - 6 + 5 = 2 x - 1$ $y=2(x-3)+5=2x-6+5=2x-1$

If $x < 3$ $x<3$ the the signs between the bars flip and the function becomes:
$y = 2 (- x + 3) + 5 = - 2 x + 6 + 5 = - 2 x + 11$ $y=2(-x+3)+5=-2x+6+5=-2x+11$
And then the slope is $- 2$ $-2$
graph{2|x-3|+5 [-12.8, 19.25, -1.21, 14.81]}

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How do you find the slope of $y = 2 | x - 3 | + 5$ $y=2|x-3|+5$ ?

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How do you find the slope of $y = 2 | x - 3 | + 5$ $y=2|x-3|+5$ ?