key term - Y = mx + b

Definition

The equation y = mx + b, also known as the slope-intercept form, is a linear equation that describes the relationship between two variables, x and y. This equation is fundamental in understanding and graphing linear functions, as well as finding the equation of a line given certain information.

5 Must Know Facts For Your Next Test

1. The slope-intercept form, y = mx + b, is the most common way to represent a linear equation in two variables.
2. The slope, m, determines the direction and steepness of the line, with a positive slope indicating an upward trend and a negative slope indicating a downward trend.
3. The y-intercept, b, represents the point where the line crosses the y-axis, providing the starting value of the linear function.
4. Knowing the slope and y-intercept of a line allows you to graph the line and determine its equation.
5. The slope-intercept form is useful in finding the equation of a line given two points, the slope and a point, or the y-intercept and a point.

Review Questions

• Explain how the slope-intercept form, y = mx + b, can be used to graph a linear equation.
  • The slope-intercept form, y = mx + b, provides all the necessary information to graph a linear equation. The slope, m, determines the direction and steepness of the line, while the y-intercept, b, gives the starting point where the line crosses the y-axis. By plotting the y-intercept and then using the slope to determine the direction and rate of change, you can accurately graph the linear equation represented by y = mx + b.
• Describe the process of finding the equation of a line given two points on the line.
  • To find the equation of a line given two points, (x1, y1) and (x2, y2), you can use the slope-intercept form, y = mx + b. First, calculate the slope, m, using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Then, substitute the slope and one of the given points (e.g., (x1, y1)) into the slope-intercept form to solve for the y-intercept, b. Finally, write the equation in the form y = mx + b, using the calculated slope and y-intercept.
• Analyze how the values of the slope, m, and the y-intercept, b, affect the characteristics of the linear equation y = mx + b.
  • The values of the slope, m, and the y-intercept, b, in the equation y = mx + b, significantly impact the characteristics of the linear equation. The slope, m, determines the direction and steepness of the line, with a positive slope indicating an upward trend, a negative slope indicating a downward trend, and the magnitude of the slope determining how quickly the line rises or falls. The y-intercept, b, represents the starting point of the line on the y-axis, shifting the entire line up or down without changing its direction or steepness. Together, the slope and y-intercept define the unique characteristics of the linear equation, allowing you to graph the line and understand its behavior.

Related terms

Slope:

The slope, represented by the variable m, indicates the rate of change or steepness of a 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, indicating the value of y when x is equal to 0.

Linear Function:

A linear function is a function where the relationship between the independent variable x and the dependent variable y can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.