Question

Lesson 6 Practice Problems

Answer 1

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 $y/x=k$ or $y=kx$

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

$y=3x$

What the slope and intercept mean in each situation

The slope is

$m=\frac{3}{1}=3$

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.