Question

The population of birds in a sanctuary Increases at a steady rate. The graph of the population over time has the points (1, 105) and (3, 315). Name another point on the graph.

Answer 1

You could do (2, 210) or (4, 420) or (5, 525)

Answer 2

Another point on the graph is
`(0;0)`.

Explanation:

To find another point on the graph, we have to find the equations of the line.

In first place, we need to calculate the slope, which definition is:

`m=(x_(2)-x_(1))/(y_(2)-y_(1))`

The problem gives us the two points needed to find the slope:

`m=(x_(2)-x_(1))/(y_(2)-y_(1))\\m=(315-105)/(3-1)=(210)/(2)=105`

Now, we use the slope and one point to find the equation with the point-slope formula:

`y-y_(1)=m(x-x_(1))\\y-105=105(x-1)\\y=105x-105+105\\y=105x`

The independent term is missing, this means that it's zero. So, when a linear function doesn't have the independent terms, we know that the line will pass through the origin of the system, which is
`(0;0)`

Therefore, another point on the graph is
`(0;0)`

(The graph is attached. The slope is two high, that's why the line is almost vertical).