Question

Sample Work Suppose you are constructing a LEGO Technic Land Rover Defender with a total of 2573 pieces. You have already put together 253 pieces. Every minute you add 5 more pieces. Part A Is the relationship linear? How do you know? ​

Answer 1

The relationship is linear.

Explanation:

A linear relationship is a trend in the data that can be modeled using a straight line, such that a relationship between two variables x and y is linear if the rate of change is constant. That is, whenever x increases by 1, and it always increases by the same constant.

The constant by which y increases as x increases by 1 is called the slope and is denoted by the letter m. Being b the y-intercept, the linear relationship is modeled by the expression:

y=m*x + b

In this case x represents the minutes and y is the total number of pieces put together, so that each time x (minutes) increases by 1, "y" increases by 5 pieces. So knowing that you have already collected 253 pieces, the expression of the linear relationship is:

y=5*x + 253

The relationship is linear.