Question

The math department sponsors a Math Family Fun Night each year. In the second year, there were 54 people present. In the fourth year, there were 100 people present. Write an equation (in any form) to represent this situation. Show any necessary work.

Answer 1

`y = 23x + 8`

Explanation:

Assuming the situation can be modelled using a linear equation, then the line must pass through the point (2,54) and (4,100).

To find the equation of this line, we determine the slope using:

`m = (y_2-y_1)/(x_2-x_1)`

Substitute the coordinates of the points:

`m = (100 - 54)/(4 - 2) = (46)/(2) = 23`

We use the following formula to find the equation of this line.

`y=m(x-x_1)+y_1`

We substitute the first point a d slope to get:

`y = 23(x - 2) + 54`

Expand the parenthesis to get:

`y = 23x - 46+ 54`

This simplifies to

`y = 23x + 8`

This is the slope-intercept from.