Question

Carlos was tracking the increasing number of people walking down the street. At 6 AM, there were 57 people. At 8 AM, there were 65 people. If Carlos made the function f(x) =4x + 33 , what would the 33 represent?

Answer 1

The equation f(x) = 4x + 33 is a linear equation in slope-intercept form.
Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.
The y-intercept, in this case, the 33, is the value of y when x = 0.
The x (input) is the number of hours past midnight, and y is the # of people.
So when x = 0, this is essentially how many people there are at midnight.
Then, for each hour past that, we add 4 more.

Answer 2

Answer: c = 33 is y-intercept in the function f(x)=4x+33.

Explanation:

Since we have given that

At 6 A.M, there were 57 people and

At 8 A.M., there were 65 people.

So, to get the rate of change we will find the slope using these data as coordinates i.e.

`(6,57)\text{ and }(8,65)`

So,

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(65-57)/(8-6)\\\\m=(8)/(2)\\\\m=4`

Now, equation of line using these 2 points is given by:

`(y-y_1)=m(x-x_1)\\\\(y-57)=4* (x-6)\\\\y-57=4x-24\\\\y=4x-24+57\\\\y=4x+33\\\\f(x)=4x+33`

which in general is the form of slope intercept form i.e.

`y=mx+c, \text{where c is y-intercept}`

So, here c=33 which represents the y-intercept .