Question

Question 8 (1 point)

Answer 1

Answer:

$P_n=10+90n$

Step-by-step explanation:

So it said it was linear and gave us two points on that line: (0,10) and (5,460).

y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.

The slope of the line can be computed using $\frac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }$.

You can also just line up the points vertically and subtract, then put 2nd difference over first difference.

Like this:

(5  ,  460)

-(0  ,    10)

--------------

5       450

So the slope is 450/5=90.

The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.

Anyways the equation is

y=90x+10

or

y=10+90x

or since we are using P and n:

$P_n=10+90n$