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

Answer:

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

Step-by-step 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:

$m=\frac{x_{2}-x_{1}}{y_{2}-y_{1}}$

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

$m=\frac{x_{2}-x_{1}}{y_{2}-y_{1}}\\m=\frac{315-105}{3-1}=\frac{210}{2}=105$

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).