Flashcard 6: System of linear equations

Front

What is the y-intercept of a linear equation?

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 does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, calculated as the rise over run (change in y over change in x).

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

Front

What does it mean if two lines intersect at a single point?

Back

If two lines intersect at a single point, it means the system of equations has one unique solution.

Front

What does it mean if two lines overlap completely?

Back

If two lines overlap completely, it means the system of equations has infinitely many solutions.

Front

How do you convert an equation to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the slope-intercept form of the equation 11x - 4y = -17?

Back

Front

What is the zero of a linear function?

Back

The zero of a linear function is the x-value where the function equals zero, also known as the x-intercept.

Front

How can you identify a system of equations from a graph?

Back

You can identify a system of equations by observing the slopes and y-intercepts of the lines in the graph.

Front

What is the graphical representation of a system with no solution?

Back

The graphical representation of a system with no solution consists of parallel lines.