Linear Equations and Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form Ax + By = C, where A, B, and C are constants.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

To determine if a point is part of the solution set for a linear inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to.' It indicates that the value on the left can be less than or equal to the value on the right.

Front

What is the graphical representation of the inequality y ≤ -¾x - 1?

Back

The graphical representation of the inequality y ≤ -¾x - 1 is a shaded region below the line y = -¾x - 1, including the line itself.

Front

How do you convert the equation 8x + 3y = 24 into slope-intercept form?

Back

To convert 8x + 3y = 24 into slope-intercept form, solve for y: 3y = -8x + 24, then y = -8/3x + 8.

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. It represents the value of y when x = 0.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the coordinate plane that satisfies the inequality, often including a boundary line.

Front

How can you identify the slope of a line from its equation in standard form?

Back

To identify the slope from an equation in standard form (Ax + By = C), rearrange it into slope-intercept form (y = mx + b) and identify m as the slope.

Front

What does it mean for a solution set to be empty?

Back

An empty solution set means that there are no values of x and y that satisfy the given equation or inequality.