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 it mean for two lines to intersect at one point?

Back

It means that the system of equations represented by the two lines has one unique solution.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables.

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and will never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations using substitution?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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

How can you determine if three points lie on the same line?

Back

You can determine this by checking if the slope between each pair of points is the same.