Understanding Linear Equations and Solutions

What is a linear equation primarily characterized by?

• It includes variables x and y and forms a straight line.

• It has only one variable.

• It forms a circle on a graph.

• It forms a parabola on a graph.

How can you determine if a point like (2, 11) satisfies the equation y = 3x + 5?

• By checking if 2 + 11 equals 5.

• By substituting x with 2 and y with 11 and verifying both sides of the equation.

• By graphing the equation and seeing if the point lies on the line.

• By checking if 3 times 11 equals 2.

What is the result when you substitute x = 4 and y = 16 into the equation y = 7x - 3?

• 16 equals 28, so it does not satisfy the equation.

• 16 equals 25, so it does not satisfy the equation.

• 16 equals 28, so it satisfies the equation.

• 16 equals 25, so it satisfies the equation.

When dealing with equations involving large numbers, what is a recommended approach?

• Always use a graph to verify.

• Use a calculator to simplify and verify the solution.

• Ignore the large numbers and focus on smaller ones.

• Assume the solution is correct without verification.

What should you be cautious of when verifying solutions to equations with large numbers?

• The possibility of arithmetic errors.

• The belief that large numbers simplify the process.

• The need to always graph the equation.

• The assumption that all large numbers are solutions.