Verify Solutions of Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What does it mean to verify a solution of a linear equation?

Back

Verifying a solution means substituting the coordinates (x, y) into the equation to check if both sides are equal.

Front

How do you verify if the coordinates (-1, 4) are a solution to the equation 5x - 2y = -13?

Back

Substitute x = -1 and y = 4 into the equation: 5(-1) - 2(4) = -5 - 8 = -13. Since both sides are equal, the coordinates are a solution.

Front

What is the result of substituting (0, -2) into the equation -3x + 4y = 8?

Back

Substituting gives: -3(0) + 4(-2) = 0 - 8 = -8, which does not equal 8. Therefore, (0, -2) is not a solution.

Front

What is the process to check if (5, 1) is a solution to 2x - 3y = -7?

Back

Substitute x = 5 and y = 1: 2(5) - 3(1) = 10 - 3 = 7, which does not equal -7. So, (5, 1) is not a solution.

Front

What does it mean if a point lies on the line of a linear equation?

Back

If a point lies on the line, it means that the coordinates of that point satisfy the equation of the line.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you determine if a point is a solution without graphing?

Back

You can determine if a point is a solution by substituting the x and y values into the equation and checking if both sides are equal.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.