Review Linear Equations

What is the y-intercept in the context of a linear equation?

• The point where the line crosses the x-axis.

• The point where the line crosses the y-axis. It represents the value of the dependent variable when the independent variable is zero.

• The slope of the line when the independent variable is zero.

• The value of the independent variable when the dependent variable is zero.

How can you represent a linear equation graphically?

• As a straight line on a coordinate plane, where the x-axis represents the independent variable and the y-axis represents the dependent variable.

• As a curve that varies with the x-axis and y-axis values.

• As a series of points plotted randomly on a graph.

• As a vertical line indicating the value of the dependent variable.

What is the process of substitution in solving systems of linear equations?

• Substitution involves solving one equation for one variable and then substituting that expression into another equation to find the values of the variables.

• Substitution requires adding the equations together to eliminate one variable.

• Substitution is the method of multiplying both equations by a common factor to find the solution.

• Substitution means replacing one variable with a constant value to simplify the equations.

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

• It represents the y-intercept of the equation.

• It indicates the rate of change between the two variables.

• It shows the maximum value of the function.

• It determines the direction of the graph.

What does it mean for two quantities to be equal in a linear equation?

• They represent different values that can be substituted into the equation.

• They represent the same value, meaning the equation holds true when the values are substituted for the variables.

• They are always equal regardless of the values of the variables.

• They are equal only when the equation is simplified.

How do you solve a linear equation with one variable?

• Isolate the variable on one side using inverse operations until it is alone.

• Add the same number to both sides of the equation only.

• Multiply both sides by the same number without changing the equation.

• Subtract the variable from both sides to eliminate it.

What is the elimination method in solving systems of linear equations?

• The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

• The elimination method requires multiplying both equations by a constant to make the coefficients equal.

• The elimination method is a graphical approach to find the intersection of two lines.

• The elimination method is used to convert a system of equations into a single equation.

How do you translate a word problem into a linear equation?

• Identify the variables, determine the relationships between them, and express these relationships mathematically.

• Write down the problem statement without any changes.

• Use a graph to represent the problem visually.

• Ignore the context and focus only on the numbers provided.

What is the role of constants in a linear equation?

• Constants are variable values that change with the equation.

• Constants are fixed values that do not change and help define the specific line represented by the equation.

• Constants are used to represent the slope of the line.

• Constants are only used in quadratic equations.

What does it mean for a linear equation to have infinitely many solutions?

• A linear equation has infinitely many solutions when it has no solutions at all.

• A linear equation has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

• A linear equation has infinitely many solutions when it has exactly one solution.

• A linear equation has infinitely many solutions when the slope of the line is zero.