8th Math Mid-Term Exam Study Guide Part 2

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 is a linear function?

Back

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

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, they will have infinitely many solutions because every point on the line is a solution.

Front

What is the difference between linear and nonlinear equations?

Back

Linear equations graph as straight lines, while nonlinear equations graph as curves or other shapes.

Front

What does it mean to solve by inspection?

Back

Solving by inspection means to find the solution by looking at the equations and identifying the solution without formal calculations.

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

How do you identify a linear equation from its graph?

Back

A linear equation will graph as a straight line, while a nonlinear equation will show curves or bends.

Front

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

Back

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

Front

What does it mean if two equations are dependent?

Back

Dependent equations are those that represent the same line, leading to infinitely many solutions.

Front

What is the graphical representation of a system with one solution?

Back

The lines representing the equations intersect at exactly one point.