Unit Test: Systems of Linear Equations & Linear Transformations

Front

What is a system of linear equations?

Back

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

Front

How do you find the solution to a system of linear equations graphically?

Back

By graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What effect does a positive slope have on the graph of a linear equation?

Back

A positive slope means the line rises from left to right.

Front

What effect does a negative slope have on the graph of a linear equation?

Back

A negative slope means the line falls from left to right.

Front

What is a vertical stretch in the context of linear transformations?

Back

A vertical stretch occurs when the slope of the line is multiplied by a factor greater than 1, making the line steeper.

Front

What is a vertical compression in the context of linear transformations?

Back

A vertical compression occurs when the slope of the line is multiplied by a factor between 0 and 1, making the line less steep.

Front

What does reflection across the x-axis mean for a linear function?

Back

Reflection across the x-axis means that the y-values of the function are multiplied by -1, resulting in an inverted graph.