Linear Equations: y = mx

A linear equation in the form y = mx, where 'm' represents the slope.

The rate of change of a line, calculated as the rise over run.

The point where the x and y axes intersect, with coordinates (0, 0).

A straight line that passes through the origin (0, 0).

The process of identifying the equation of a line from its graph.

The first step in finding the equation of a line from its graph is to determine its slope.

The second step in finding the equation of a line from its graph is to use the slope and the fact that the line passes through the origin.

The process of creating a visual representation of a linear equation.

The first step in graphing an equation is to create a table of values.

The second step in graphing an equation is to plot the points from the table on a coordinate plane.

A linear equation in which the slope is determined by dividing the difference in y-values by the difference in x-values between two points on the line.

The equation y = 12.5x represents the relationship between the number of gallons of water used and the time spent watering.

The equation y = -1/2x represents the relationship between the number of hours spent on homework and the number of problems completed.

The equation y = -5x represents the relationship between the time spent driving and the distance driven.

The equation y = 3/5x represents the relationship between the number of cookies baked and the amount of flour used.

A graphical representation of a linear equation that does not accurately reflect the equation's properties, particularly the slope.

The term 'proportional' indicates a direct relationship between two variables.

The term 'linear' indicates a relationship that can be represented by a straight line on a graph.

A key characteristic of linear equations is that they can be represented as a straight line on a graph.

The ability to predict future values based on the relationship between two variables, represented by a linear equation.

A linear equation in the form y = mx + b represents a relationship between two variables, where 'm' is the slope and 'b' is the y-intercept.

The point where the line intersects the y-axis, represented by the value 'b' in the equation y = mx + b.

The value 'b' in the equation y = mx + b represents the initial value of the dependent variable.

The 'constant' value in a linear equation represents the y-intercept, the value of y when x is zero.

The form of linear equations, 'y = mx + b,' is significant because it allows for easy identification of the slope and y-intercept.

The slope of a line determines the direction and steepness of the line.

Understanding the slope of a line can be beneficial in various real-world applications, such as analyzing trends in data, predicting future outcomes, or making informed decisions.

Understanding and manipulating linear equations is a key skill in mathematics and can be useful in various fields such as science, engineering, business, and economics.

The ability to accurately interpret linear equations and their graphs is essential for understanding mathematical concepts and solving problems effectively.