EOC Category 3 - Writing & Solving Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means one line rises while the other falls.

Front

How can you determine if a point (x, y) is a solution to a linear equation?

Back

To determine if (x, y) is a solution, substitute x into the equation and see if the resulting y value matches the y in the point.

Front

What is the process for solving a system of equations by substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the process for solving a system of equations by elimination?

Back

To solve by elimination, manipulate the equations to eliminate one variable, allowing you to solve for the other variable.