Exercise 44 Page 213

We are asked to find the slope of the line we would get if we graphed the sequences shown below and connected the points. If the sequences represent linear relations, then we can find the value of the associated line's slope by using any two terms of the sequence. Let's recall the Slope Formula. In the equation, $m$ is the slope of the line and $(x_1,y_1)$ and $(x_2,y_2)$ are two known points on the line. In the sequence, the term number would represent the $x\text{-}$coordinate and the term value would be the associated $y\text{-}$coordinate. We will now find the slope for Sequence A using the first two terms, which are equivalent to $(1,5)$ and $(2,8).$ The slope for the line associated with Sequence A is $m=3.$ Notice that if we use any two consecutive terms the denominator in the Slope Formula will always be one. Therefore, the value for the slope is just the common difference of the sequence, obtained as any term minus its previous term. We can use this to find the slope for the rest of sequences.

Sequence	Common difference	Slope
$\text{a. }5,8,11,14,\dots$	$8-5=3$	$m_a=3$
$\text{b. }3,9,15,\dots$	$9-3=6$	$m_b=6$
$\text{c. }26,21,16,\dots$	$21-26=\text{-}5$	$m_c=\text{-}5$
$\text{d. }7,8.5,10,\dots$	$8.5-7=1.5$	$m_d=1.5$