Unit 4: Linear Equations and Linear Systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does 'slope' represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in the slope-intercept form of a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

What does it mean for a system of equations to have 'no solutions'?

Back

A system of equations has no solutions when the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have 'many solutions'?

Back

A system of equations has many solutions when the equations represent the same line, meaning they overlap completely.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if two linear equations are equivalent?

Back

Two linear equations are equivalent if they have the same slope and y-intercept, meaning they represent the same line.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What is the difference between intersecting lines and parallel lines in terms of solutions?

Back

Intersecting lines represent a system with one solution (the point of intersection), while parallel lines represent a system with no solutions.

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).