We can use two data points to find the linear function that relates the two quantities. For example, a linear function relating calories (C) consumed over days(d) can be generated from the following data: -After 3 days 4,100 calories have been consumed. -After 8 days 10,600 calories have been consumed. The slope of this function is and indicates the number of calories consumed each day. The y-intercept of this function is and indicates the calories consumed at day . This function can be modeled by C=

Step-by-step explanation:

Let the number of days be x because x is the independent variable

Any y is the number of calories consumed the dependent variable.

Now slope = y2 - y2/ x2 - x2

= 10600-4100/8-3

= 6500/5 = 1300

From our analysis we know it consumes 1300 per day so ideally on day 3 we expect him to consume 1300x3= 3900

But the given value is 4100

This means it's inherent energy is 4100-3900= 200

This is the y- intercept and it occurs when x= 0

from the above explanation we know that

C = 200. and it's the y- intercept.

Look at the general equation of a line

y = mx + C; when x= 0, y = C; note we define C as the value of y when x = 0