Question

What is the slope of the line in this graph?
The table shows the balance of Steven's savings account over time. Assuming there are no withdrawals, if you graph the relationship for Steven's monthly balances, which points will lie on the resulting line?

Month Balance
1 $400
3 $1,200
7 $2,800
9 $3,600
13 $5,200

Answer 1

Answer:

It looks like both B and D are correct answers. because 23*400=9200 and 26*400=10400

Step-by-step explanation:

If a line passing through two points then the equation of line is

Choose any two points from the given table.

Let the two points are (1,400) and (3,1200).

The equation of line is

Steven's monthly balances is defined by the equation

At x=22,

At x=23,

At x=24,

At x=26,

At x=27,

The points (23, 9,200) and (26, 10,400) lie on the line. Therefore the correct options are B and D.

Answer 2

Answer:

400

Step-by-step explanation:

The formula we should use is: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ where (x1, y1) and (x2, y2) are any two points on the line and m is the slope of the line.

If we treat the month to be the variable along the x-axis, and the balance to be the variable along the y-axis, then we can apply the formula.

Substituting the first two entries into the equation:

$m = \frac{1200 - 400}{3 - 1} = 400$

It should be noted that any two entries in the table will yield the same result, because slope is a ratio, but we choose the first two because the calculation is easier.