Write An Equation To Represent This Situation.$y = 25x + 100$

Introduction

In mathematics, a linear equation is a type of equation that can be written in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. The equation $y = 25x + 100$ is a linear equation that represents a straight line on a coordinate plane. In this article, we will explore the concept of linear equations, the components of the equation $y = 25x + 100$, and how to use it to solve problems.

What is a Linear Equation?

A linear equation is an equation that can be written in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. The slope of a line is a measure of how steep the line is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run). The y-intercept is the point at which the line intersects the y-axis.

Components of the Equation $y = 25x + 100$

The equation $y = 25x + 100$ is a linear equation that has two components: the slope ($m$) and the y-intercept ($b$). In this equation, the slope is 25 and the y-intercept is 100.

• Slope (m): The slope of the line is 25, which means that for every unit increase in $x$, the value of $y$ increases by 25 units.
• Y-intercept (b): The y-intercept of the line is 100, which means that the line intersects the y-axis at the point (0, 100).

Graphing the Equation $y = 25x + 100$

To graph the equation $y = 25x + 100$, we can use the slope-intercept form of a linear equation. The slope-intercept form is given by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• Plotting the y-intercept: The y-intercept is the point at which the line intersects the y-axis. In this case, the y-intercept is (0, 100), which means that the line intersects the y-axis at the point (0, 100).
• Plotting the slope: The slope of the line is 25, which means that for every unit increase in $x$, the value of $y$ increases by 25 units. To plot the slope, we can start at the y-intercept (0, 100) and move 1 unit to the right. The new point is (1, 125).
• Plotting additional points: To plot additional points, we can continue to move 1 unit to the right and calculate the corresponding value of $y$. For example, if we move 2 units to the right, the new point is (2, 150).

Solving Problems Using the Equation $y = 25x + 100$

The equation $y = 25x + 100$ can be used to solve a variety of problems. Here are a few examples:

• Finding the value of $y$: If we know the value of $x$, we can use the equation $y = 25x + 100$ to find the corresponding value of $y$.
• Finding the value of $x$: If we know the value of $y$, we can use the equation $y = 25x + 100$ to find the corresponding value of $x$.
• Graphing the equation: We can use the equation $y = 25x + 100$ to graph the line on a coordinate plane.

Real-World Applications of the Equation $y = 25x + 100$

The equation $y = 25x + 100$ has a variety of real-world applications. Here are a few examples:

• Cost and revenue: The equation $y = 25x + 100$ can be used to model the cost and revenue of a business. For example, if the cost of producing $x$ units of a product is $25x + 100$, we can use the equation to find the total cost of producing a certain number of units.
• Distance and speed: The equation $y = 25x + 100$ can be used to model the distance and speed of an object. For example, if an object is traveling at a speed of 25 units per hour, we can use the equation to find the distance traveled in a certain number of hours.
• Finance: The equation $y = 25x + 100$ can be used to model the growth of an investment. For example, if an investment is growing at a rate of 25% per year, we can use the equation to find the future value of the investment.

Conclusion

Q: What is the slope of the line represented by the equation $y = 25x + 100$?

A: The slope of the line represented by the equation $y = 25x + 100$ is 25. This means that for every unit increase in $x$, the value of $y$ increases by 25 units.

Q: What is the y-intercept of the line represented by the equation $y = 25x + 100$?

A: The y-intercept of the line represented by the equation $y = 25x + 100$ is 100. This means that the line intersects the y-axis at the point (0, 100).

Q: How do I graph the equation $y = 25x + 100$?

A: To graph the equation $y = 25x + 100$, you can use the slope-intercept form of a linear equation. Plot the y-intercept (0, 100) and then plot additional points by moving 1 unit to the right and calculating the corresponding value of $y$.

Q: How do I find the value of $y$ if I know the value of $x$?

A: To find the value of $y$ if you know the value of $x$, you can plug the value of $x$ into the equation $y = 25x + 100$ and solve for $y$.

Q: How do I find the value of $x$ if I know the value of $y$?

A: To find the value of $x$ if you know the value of $y$, you can plug the value of $y$ into the equation $y = 25x + 100$ and solve for $x$.

Q: What are some real-world applications of the equation $y = 25x + 100$?

A: Some real-world applications of the equation $y = 25x + 100$ include:

• Cost and revenue: The equation can be used to model the cost and revenue of a business.
• Distance and speed: The equation can be used to model the distance and speed of an object.
• Finance: The equation can be used to model the growth of an investment.

Q: Can I use the equation $y = 25x + 100$ to solve problems that involve non-linear relationships?

A: No, the equation $y = 25x + 100$ is a linear equation and can only be used to solve problems that involve linear relationships. If you need to solve a problem that involves a non-linear relationship, you will need to use a different type of equation.

Q: Can I use the equation $y = 25x + 100$ to solve problems that involve multiple variables?

A: No, the equation $y = 25x + 100$ is a single-variable equation and can only be used to solve problems that involve a single variable. If you need to solve a problem that involves multiple variables, you will need to use a different type of equation.

Q: How do I know if the equation $y = 25x + 100$ is a good model for a particular problem?

A: To determine if the equation $y = 25x + 100$ is a good model for a particular problem, you can use the following criteria:

• Does the equation accurately represent the relationship between the variables?
• Does the equation make sense in the context of the problem?
• Does the equation produce reasonable results when used to solve the problem?

If the equation meets these criteria, it is likely a good model for the problem.