Answer:
see the procedure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Remember that
An equilateral triangle has three equal sides
Let
x -----> the length side of an equilateral triangle in units
y ----> the perimeter of an equilateral triangle
If the y-intercept is the point (0,0)
then
The linear equation passes through the origin
so
This problem represent a proportional relationship between the variables x and y
we have that
The slope is equal to 3
so
The linear equation is
[tex]y=3x[/tex]
What the slope and intercept mean in each situation
The slope is
[tex]m=\frac{3}{1}=3[/tex]
That means -----> The perimeter and the length side of an equilateral triangle have the ratio of 3:1
so
The perimeter is three times the length side of an equilateral triangle
The y-intercept is the value of y when the value of x is equal to zero
In this problem
The y-intercept is the value of the perimeter of an equilateral triangle, when the value of the length side is equal to zero
The y-intercept is (0,0), that means that the perimeter of an equilateral triangle is zero, when the value of the length side is equal to zero, because
both variables represent a proportional relationship.
