Question

the terms in sequence A increases by 3. The terms in sequence B increase by 8. In which sequence do the terms form a steeper line when graphed as points on a coordinate plane? Justify your reasoning.

Answer 1

Solution: The sequence B shows the steeper line.

Exanation:

The line having greater slope is always steeper than the other lines.

Since it is given that the sequence A increases by 3 and the sequence B increases by 8. It means for each additional value the sequences increased by 3 and 5 units respectively.

The slope of line is rate of change of one variable with respect to another variable.

The sequence A increased by 3, therefore the slope of line of sequence A is 3.

The sequence B increased by 8, therefore the slope of line of sequence B is 8.

Since the slope of sequence B is greater than the slope of sequence A, therefore the line of sequence B is steeper than the line of sequence A.

The sequence A can be defined as 3,6,9,12,.... and the sequence B can be defined as 8,16,24,....

So the coordinates points of sequence A are (0,0)(1,3),(2,6) and the coordinates points of sequence B are (0,0),(1,8),(2,16).

From the given figure it is notes that the blue line is steeper than red line.

Therefore, the sequence B shows the steeper line.