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

Oct 3, 2016

This one has two slopes

Explanation:

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

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