Question

Which of the following statements about the given graph is correct?

Answer 1

The given graph is linear but the slope changes at \(x\) =3.
Let’s calculate the slope when \(x<3.\)
Let’s pick $2$ points, say $(1, 2)$ and $(2, 1)$.

\(\textrm{Slope} =\dfrac{\textrm{change in y-coordinates}}{\textrm{change in x-coordinates}} = \dfrac{2-1}{1-2} =\dfrac{1}{-1}= -1\)

Now, let’s calculate the slope when \(x>3.\)
Let’s pick $2$ points, say $(4, 1)$ and $(5, 2)$.

\(\textrm{Slope} =\dfrac{\textrm{change in y-coordinates}}{\textrm{change in x-coordinates}} = \dfrac{2-1}{5-4}=\dfrac{1}{1}=1\)

Therefore, the statement “When \(x<3\), the slope is \(-1\)” is correct.