Respuesta :
Answer:
[tex]P_n=10+90n[/tex]
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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }[/tex].
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:
[tex]P_n=10+90n[/tex]
