please justify your reasoning please please please

Question

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The terms in arithmetic Sequence A have a common difference of 3.The terms in arithmetic Sequence B have a common difference of 8. In which sequence do the terms form a steeper line when graphed as points on a coordinate plane? Justify your reasonin.

Answer 1

If the terms in each sequence are numbered sequentially and the term is the y-value and the sequence number is the x-value [note: points in the Cartesian Coordinate System are represented by (x,y) and the slope (that is, the "steepness", or incline, or grade, etc.) is (y₂ - y₁) / (x₂ - x₁) ], then the slope will be steeper when the common difference is larger.  Also note that a negative common difference means a negative slope.

 

Sequence B, with a common difference of 8. has a slope of 8 [quite steep].  Sequence A, with a common difference of 3, has a slope that is less steep.  Note that slope is often called "rise over run."