Question

Andy joins a social networking site. After day three, he has 25 friends; after day eight, he has 40 friends. Write the equation to show the number of friends he will have on day 18 if he continues to add the same number of friends each day.

Answer 1

Answer:

Point slope intercept form: The equation for line is given by; $y-y_1=m(x-x_1)$ ......[1] ; where m is the slope and a point $(x_1, y_1)$ 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);

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given values we get;

$m = \frac{40-25}{8-3}=\frac{15}{5}$ = 3

now, substitute the given values of m=3 and a point (3, 25) in [1] we get;

$y-25=3(x-3)$

Using distributive property; $a \cdot(b+c) = a\cdot b + a\cdot c$

$y-25 = 3x - 9$

Add 25 on both sides, we get;

$y-25+25 = 3x - 9+25$

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.