Question

You are pouring 50 pounds of sand into a wagon. The linear function $y=10x$ represents the weight $y$ (in pounds) of the sand in the wagon after you have poured $x$ bags of sand into the wagon.

Answer 1

The question requires understanding and applying the concepts of linear equations, specifically focusing on identifying independent and dependent variables, and interpreting the slope and y-intercept in different real-world contexts.

Step-by-step explanation:

This question covers several types of linear equations and explores concepts such as independent and dependent variables, the slope and y-intercept of a linear function, and their application in various real-world scenarios. We handle different situations including the loss of soil due to erosion, labor charges based on hours worked, and understanding weight and force. For each of these scenarios, we apply our knowledge of linear functions to analyze and interpret the given information.

Examples of Linear Equations:

1. For soil erosion, the equation y = 12,000x could represent the total amount of soil lost per year, with x as the number of years and y as the total soil lost.
2. In the context of labor charges, y = 55x + 75 relates hours worked on a car (x) with the total labor charges (y).
3. The relationship between an applied force (F1) and the mass of bricks in a wheelbarrow can be deduced by considering the total weight and the gravitational pull.

Understanding these concepts allows students to interpret and solve problems that can be modeled by linear equations, an essential part of algebra and real-world problem-solving.

Answer 2

50

Step-by-step explanation:

50-