Graphing Systems of Equations

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines are intersecting.

Front

What is the solution to the system of equations represented by the point (-3, -8)?

Back

The solution is the point where the two lines intersect at (-3, -8).

Front

How can you determine the equation of a line from a graph?

Back

By identifying the slope and y-intercept from the graph.

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 does the solution (x, y) to a system of equations represent?

Back

It represents the point where the two lines intersect.

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines have no solutions because they never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The two lines coincide, meaning they are the same line.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the line represented by the equation y = 2x + 3?

Back

The y-intercept is 3.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

Rearrange the equation to solve for y in terms of x.