Answer:
Point slope intercept form: The equation for line is given by;
......[1] ; where m is the slope and a point
on the line.
Let x represents the number of days and y represents the number of friends.
As per the statement: After day three, he has 25 friends; after day eight, he has 40 friends.
⇒ We have two points i.e,
(3, 25) and (8, 40)
First calculate slope(m);
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute the given values we get;
= 3
now, substitute the given values of m=3 and a point (3, 25) in [1] we get;
![y-25=3(x-3)](https://tex.z-dn.net/?f=y-25%3D3%28x-3%29)
Using distributive property; ![a \cdot(b+c) = a\cdot b + a\cdot c](https://tex.z-dn.net/?f=a%20%5Ccdot%28b%2Bc%29%20%3D%20a%5Ccdot%20b%20%2B%20a%5Ccdot%20c)
![y-25 = 3x - 9](https://tex.z-dn.net/?f=y-25%20%3D%203x%20-%209)
Add 25 on both sides, we get;
![y-25+25 = 3x - 9+25](https://tex.z-dn.net/?f=y-25%2B25%20%3D%203x%20-%209%2B25)
Simplify:
y =3x + 16
if x = 18 days, then;
y = 3(18) + 16 = 54+16 = 70
Therefore, he will have on day 18, if he continues to add the same number of friends each day is, 70 friends.