Solving Systems by Graphing

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Front

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

Back

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

Front

What does the slope-intercept form of a linear equation represent?

Back

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

Front

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

Back

The slope of the line is 2.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the intersection point of two lines?

Back

The intersection point of two lines is the point where the two lines meet, representing the solution to the system of equations.

Front

How can you find the intersection point of two linear equations graphically?

Back

You can find the intersection point by graphing both equations on the same coordinate plane and identifying the point where they cross.

Front

What does it mean if two equations represent the same line?

Back

If two equations represent the same line, they have infinite solutions because every point on the line is a solution.

Front

How do you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel and do not intersect.