Question

Marina earns $15 for 1 hour of babysitting $23 for 2 hours of babysitting and $31 for 3 hours of babysitting. Write a function to describe the sequence.

Answer 1

Explanation:

Let y represent the amount that Marina earns for babysitting.

Let x represent the number of hours of babysitting.

If we plot the graph of y on the vertical axis and x on the horizontal axis of a graph,

the slope which is expressed as

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

Slope = (23 - 15)/(2 - 1) = 8

We would model the function in the slope intercept form which is expressed as

y = mx + c

Where c represents the intercept.

To determine c, we would substitute y = 15, x = 1 and m = 8 into y =mx + c. It becomes

15 = 8 × 1 + c

15 = 8 + c

c = 15 - 8 = 7

The function that describes the sequence would be

y = 8x + 7