Graphing Gas: Decoding Y = -1/20x + 10 For Michelle's Car

Hey everyone! Let's dive into a fun math problem that's super relevant to real life – figuring out how much gas Michelle has left in her car after driving a certain distance. We're given the equation y = -1/20x + 10, which represents the gallons of gasoline (y) remaining after Michelle drives x miles. The big question is: Which graph perfectly captures this equation and visually shows us how Michelle's gas tank empties? Let's break this down step-by-step, making sure we understand the equation, what it means, and how to find the right graph.

Understanding the Equation: y = -1/20x + 10

So, at first glance, the equation y = -1/20x + 10 might look a bit intimidating, but trust me, it's simpler than it seems. This equation is written in what we call slope-intercept form, which is a super handy way to represent linear relationships. Linear relationships, in this case, show a constant rate of change – Michelle's car consumes gas at a steady pace as she drives. The slope-intercept form is generally written as y = mx + b, where:

• y represents the dependent variable (the gallons of gas remaining). This is what we're trying to find based on the number of miles driven.
• x represents the independent variable (the miles Michelle drives). This is the variable we can change or choose.
• m represents the slope of the line. The slope tells us how much y changes for every one unit change in x. In our case, it tells us how many gallons of gas are used per mile driven.
• b represents the y-intercept. The y-intercept is the value of y when x is zero. In other words, it's the amount of gas Michelle has in her car when she hasn't driven any miles yet.

Key Takeaways: Understanding the equation is crucial. In our equation, y = -1/20x + 10, we can quickly identify the slope and the y-intercept. The slope (m) is -1/20, and the y-intercept (b) is 10. This is super important information because it tells us two things right off the bat: Michelle starts with 10 gallons of gas (the y-intercept), and for every 20 miles she drives, she uses 1 gallon of gas (the slope). The negative sign in front of the slope indicates that the amount of gas is decreasing as the miles driven increase, which makes perfect sense. Now, let's visualize this. If we were to graph this equation, we'd see a straight line sloping downwards. The steeper the slope (ignoring the negative sign for now), the faster the gas is being used. A gentler slope would mean the gas is being used more slowly. In this case, -1/20 isn't a very steep slope, meaning the line will decline gradually. This also gives us a clue about what the graph will look like: a line that starts at the y-axis at the 10-gallon mark and gradually slopes downwards as we move to the right (increasing the number of miles driven).

Deciphering the Slope: -1/20

Let's zoom in on that slope, m = -1/20, because it’s packed with information. The slope is the heart of understanding how the amount of gas in Michelle's car changes as she drives. Remember, the slope is often described as