Fiona wrote the linear equation y 2 5x 5 – Fiona’s linear equation, y = 2 + 5x – 5, embarks us on a mathematical odyssey that delves into the intricacies of linear equations and their applications. This equation, seemingly simple yet profound, holds the key to understanding the relationship between variables, graphing linear functions, and solving real-world problems.
As we embark on this exploration, we will dissect Fiona’s equation, unraveling its components and uncovering its significance. We will delve into the concept of slope and y-intercept, providing a comprehensive understanding of their roles in shaping the equation’s behavior.
Linear Equations: Fiona Wrote The Linear Equation Y 2 5x 5
Linear equations are mathematical equations that represent a straight line. They are of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, while the y-intercept represents the value of y when x = 0.
Slope-Intercept Form
The slope-intercept form of a linear equation is the most common form. It is written as y = mx + b, where m is the slope and b is the y-intercept. The slope is calculated by dividing the change in y by the change in x, and the y-intercept is the value of y when x = 0.
Fiona’s Equation, Fiona wrote the linear equation y 2 5x 5
The given equation, y = 2 + 5x – 5, is in slope-intercept form. The slope of the line is 5, and the y-intercept is -3. This means that the line rises 5 units for every 1 unit increase in x, and it crosses the y-axis at -3.
Graphing the Equation
To graph the equation y = 2 + 5x – 5, follow these steps:
- Plot the y-intercept at (0, -3).
- Use the slope to find another point on the line. Since the slope is 5, move up 5 units and right 1 unit from the y-intercept to get the point (1, 2).
- Draw a straight line through the two points.
Applications of the Equation
Linear equations have many applications in real-world situations. For example, they can be used to model the relationship between the distance traveled and the time taken, or the relationship between the cost of a product and the number of units purchased.
Essential FAQs
What is the slope of Fiona’s equation?
The slope of the equation y = 2 + 5x – 5 is 5.
What is the y-intercept of Fiona’s equation?
The y-intercept of the equation y = 2 + 5x – 5 is 2.
How do you graph Fiona’s equation?
To graph the equation y = 2 + 5x – 5, plot the y-intercept (0, 2) and use the slope (5) to draw a line.
