Solutions to Equations in Two Variables

Front

What is an ordered pair in the context of equations in two variables?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on a coordinate plane, where 'x' is the value on the horizontal axis and 'y' is the value on the vertical axis.

Front

How do you determine if an ordered pair is a solution to an equation?

Back

To determine if an ordered pair (x, y) is a solution to an equation, substitute the values of x and y into the equation. If the equation holds true, then the ordered pair is a solution.

Front

What does it mean for an ordered pair to NOT be a solution to an equation?

Back

An ordered pair (x, y) is NOT a solution to an equation if substituting x and y into the equation does not satisfy the equation, meaning the left side does not equal the right side.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What is the significance of the slope in a linear equation?

Back

The slope of a linear equation indicates the steepness and direction of the line. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

How can you verify if a point lies on a line represented by an equation?

Back

To verify if a point (x, y) lies on a line, substitute the x-value into the equation and check if the resulting y-value matches the y-value of the point.

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

What is the relationship between the coefficients in the equation of a line and its graph?

Back

The coefficients in the equation of a line determine the slope and y-intercept, which directly affect the graph's appearance and position on the coordinate plane.

Front

What does it mean for a solution to be 'TRUE' in the context of equations?

Back

A solution is 'TRUE' when the ordered pair satisfies the equation, meaning that substituting the values results in a true statement.