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 should be non-negative.

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 to isolate it on one side of the equation.

Front

What does the intersection point of two lines represent in a system of equations?

Back

The intersection point represents the solution to the system of equations, indicating the values of x and y that satisfy both equations.

Front

What is slope-intercept form of a linear equation?

Back

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

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 but different y-intercepts, resulting in no solution for the system of equations.

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel, meaning they never intersect.

Front

What is the y-intercept of the equation y = -3x + 12?

Back

The y-intercept is the point where the line crosses the y-axis, which is (0, 12) for the equation y = -3x + 12.

Front

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

Back

To find the solution graphically, plot both equations on the same graph and identify the point where the two lines intersect.

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

The coefficients A and B determine the slope and position of the line in the coordinate plane.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.