Answer:
The 30th term is 148. The change in y (3,8,13,18) is +5. Add 5 to find the number next in sequence; subtract 5 to find the number previous in sequence.
Step-by-step explanation:
Numbers in sequence 0-10: -2, 3, 8, 13, 18, 23, 28, 33, 38, 43, 48.
Numbers in sequence 11-20: 53, 58, 63, 68, 73, 78, 83, 88, 93, 98.
Numbers in sequence 21-30: 103, 108, 113, 118, 123, 128, 133, 138, 143, 148.
If you didn't notice the pattern, every +5 (<u><em>POSITIVE</em></u> +5), the number in sequence either ends in a 3 or an 8. The equation of the line would be <em>y</em>=5x+5 because the slope () is
, or 5. Applying Δ<em>y</em>/Δ<em>x</em> ("change in <em>y </em>over change in <em>x</em>": the <em>y</em>-intercept is 5 because the change in <em>y</em> is ±5 (in this explicit case: +5), and the change in <em>x</em> is ±1 (in this explicit case: +1).
The simplest way to find the equation of the line here is utilizing . You can use any two points (±) to find the slope, such as (1, 3) and (2,8) ₋ looking at the table I inserted below, you can pick any two points - for instance, 1 & 3 would be (1, 3), 2 & 8 would be (2, 8), 3 & 13 would be (3, 13), and 4 & 18 would be (4, 18). You would find the<em> y</em>-intercept by identifying the change in <em>y</em>, which I did in the paragraph above.
To find slope:
Formula to find the distance between two points:
Chosen two points: Point 1 <em>(x1,y1)</em>: (1,3) and Point 2 <em>(x2, y2)</em>: (2,8)
<em>Y2-Y1 </em>will provide the change in<em> y</em> and the rise of the slope. <em>X2-X1 </em>will provide the change in <em>x</em> and the run in slope. =
(8-3=5 and 2-1=1). Therefore, the change in <em>y</em> and rise of the slope is 5, and the change in <em>x </em>and the run in slope is 1.
simplifies to 5, so <em>the slope is 5.</em>
The change in <em>y</em> provides the <em>y</em>-intercept. The change in <em>y</em> is 5.
<u>Identifying slope and the </u><em><u>y</u></em><u>-intercept</u>
<em>y=mx+b</em> is the formula for slope and <em>y</em>-intercept, AKA slope-intercept form.
<em>M</em> is the slope of the line, and <em>b</em> is the <em>y</em>-intercept, or the change in <em>y</em>. The <em>y</em>-intercept of this line is the value of <em>y</em> at the point where the line crosses the<em> y </em>axis. The <em>y</em> before the sign of equality (=) will stay as <em>y, </em>and the <em>x </em>after <em>m,</em> or the slope, will stay as <em>x</em>. It means<em> y-axis=(m)x</em>-axis<em> + (b).</em>
<u>Equation of the Line</u>
Therefore, the equation of the line is<em> y=5x+5. </em>I inserted a graph below in which I graphed the equation of the line, as well as a table for the terms.
