Exercise 4.3.25

3 points on a linewill give equal slopes $\left(b_2-b_1\right)∕\left(t_2-t_1\right)=\left(b_3-b_2\right)∕\left(t_3-t_2\right)$. Linear algebra: Orthogonal to the columns $(1,1,1)$ and $\left(t_1,t_2,t_3\right)$ is $y=(t_2-t_3,t_3-$ $t_1,t_1-t_2)$ in the left nullspace of $A$. $b$ is in the column space! Then $y^{T}b=0$ is the same equal slopes condition written as $\left(b_2-b_1\right)\left(t_3-t_2\right)=\left(b_3-b_2\right)\left(t_2-t_1\right)$.