Determine if an Ordered Pair is a Solution

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to locate a point on a coordinate plane, written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

Front

What does it mean for an ordered pair to be a solution to an equation?

Back

An ordered pair (x, y) is a solution to an equation if substituting x and y into the equation makes the equation true.

Front

How do you determine if (5, -2) is a solution to the equation x - y = 7?

Back

Substitute x = 5 and y = -2 into the equation: 5 - (-2) = 7, which simplifies to 5 + 2 = 7. Since this is true, (5, -2) is a solution.

Front

What is the first step to check if (3, 4) is a solution to the equation 2x + 3y = 24?

Back

Substitute x = 3 and y = 4 into the equation: 2(3) + 3(4) = 24.

Front

What is the result of substituting (5, 4) into the equation y = x + 1?

Back

Substituting gives 4 = 5 + 1, which simplifies to 4 = 6. This is false, so (5, 4) is not a solution.

Front

What does it mean if an ordered pair does not satisfy an equation?

Back

It means that substituting the values of the ordered pair into the equation does not result in a true statement.

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

How can you verify if (3, 4) is a solution to the equation 2x + 3y = 24?

Back

Calculate: 2(3) + 3(4) = 6 + 12 = 18, which is not equal to 24. Therefore, (3, 4) is not a solution.

Front

What is the significance of the y-intercept 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 = 0.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form Ax + By = C.