The <em>first</em> series uses a <em>linear</em> function with - 1 as <em>first</em> element and 1 as <em>common</em> difference, then the rule corresponding to the series is y = |- 1 + x|.
The <em>second</em> series uses a <em>linear</em> function with - 3 as <em>second</em> element as 2 as <em>common</em> difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
<h3>What is the pattern and the function behind a given series?</h3>
In this problem we have two cases of <em>arithmetic</em> series, which are sets of elements generated by a condition in the form of <em>linear</em> function and inside <em>absolute</em> power. <em>Linear</em> <em>functions</em> used in these series are of the form:
y = a + r · x (1)
Where:
a - Value of the first element of the series.
r - Common difference between two consecutive numbers of the series.
x - Index of the element of the series.
The <em>first</em> series uses a <em>linear</em> function with - 1 as <em>first</em> element and 1 as <em>common</em> difference, then the rule corresponding to the series is y = |- 1 + x|.
The <em>second</em> series uses a <em>linear</em> function with - 3 as <em>second</em> element as 2 as <em>common</em> difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
Formula for point-slope: Plug in the values (1): {Choice B} Plug in the values (2): {Choice C} _______________________
[For (3) and (4) we need to solve for slope]
(3) First, solve for slope. Formula for slope: Plug in values: Slope: Second, we must plug into point-slope form. Formula for point-slope: Plug in the values: {Choice C}
(4) First, solve for slope. Formula for slope: Plug in values: Slope: Second, we must plug into point-slope form. Formula for point-slope: Plug in the values: {Choice D}