key term - Y=mx+b

Definition

The equation y=mx+b, known as the linear equation or the equation of a straight line, represents a linear relationship between two variables, x and y. This equation describes the relationship between the dependent variable y and the independent variable x, where m is the slope of the line and b is the y-intercept.

5 Must Know Facts For Your Next Test

1. The slope, m, determines the steepness and direction of the line. A positive slope indicates an upward-sloping line, while a negative slope indicates a downward-sloping line.
2. The y-intercept, b, represents the point where the line crosses the y-axis, indicating the value of y when x is equal to 0.
3. The equation y=mx+b can be used to model and analyze various real-world linear relationships, such as the relationship between distance, time, and speed.
4. The graph of the equation y=mx+b is a straight line, and the line can be drawn by plotting two points or by using the slope-intercept form to plot the line.
5. The equation y=mx+b is fundamental in understanding and analyzing linear functions, which are widely used in various fields, including physics, economics, and engineering.

Review Questions

• Explain the relationship between the variables x and y in the equation y=mx+b.
  • In the equation y=mx+b, the variable x is the independent variable, meaning it can be assigned any value. The variable y is the dependent variable, which means its value is determined by the value of x and the constants m and b. The slope, m, represents the rate of change between x and y, while the y-intercept, b, represents the value of y when x is equal to 0. This linear relationship between the variables x and y allows for the modeling and analysis of various real-world phenomena that can be described by a straight line.
• Describe how the values of the slope, m, and the y-intercept, b, affect the graph of the equation y=mx+b.
  • The values of the slope, m, and the y-intercept, b, in the equation y=mx+b, directly affect the graph of the line. The slope, m, determines the steepness and direction of the line. A positive slope results in an upward-sloping line, while a negative slope results in a downward-sloping line. The y-intercept, b, represents the point where the line crosses the y-axis, indicating the value of y when x is equal to 0. By knowing the values of m and b, you can plot the line on a coordinate plane and use the equation to make predictions about the relationship between the variables x and y.
• Analyze how the equation y=mx+b can be used to model and understand real-world linear relationships.
  • The equation y=mx+b is fundamental in understanding and analyzing linear relationships in various fields, such as physics, economics, and engineering. This equation can be used to model and describe real-world phenomena that exhibit a linear relationship between two variables. For example, the equation can be used to model the relationship between distance, time, and speed, where the slope, m, represents the speed, and the y-intercept, b, represents the initial position. By understanding the properties of the equation y=mx+b and how to interpret the values of m and b, you can analyze and make predictions about linear relationships in the real world, which is crucial for problem-solving and decision-making in many disciplines.

Related terms

Slope:

The slope, represented by the variable m, indicates the rate of change or the steepness of the line. It describes how the dependent variable y changes in relation to the independent variable x.

Y-intercept: The y-intercept, represented by the variable b, is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0.

Linear Function:

A linear function is a function that can be expressed in the form y=mx+b, where m and b are constant values. Linear functions produce straight lines when graphed on a coordinate plane.