Linear Equations and Inequalities Quiz

Study Notes

Linear Equations

A linear equation is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation is a straight line.
The slope of a line represents the rate of change between two points on the line. It is calculated as the change in y divided by the change in x (rise over run).
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
A horizontal line has a slope of zero.
A vertical line has an undefined slope.
Two lines are parallel if they have the same slope.
Two lines are perpendicular if the product of their slopes is -1.
Systems of linear equations consist of two or more linear equations. Solutions to systems of linear equations are points that satisfy all the equations in the system.

Linear Inequalities

A linear inequality is an inequality that can be written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants, and x and y are variables.
The graph of a linear inequality is a half-plane bounded by a line.
The boundary line is included in the graph if the inequality is "≤" or "≥"; it is excluded if the inequality is "<" or ">".
To graph a linear inequality, first graph the corresponding linear equation. Then, determine which half-plane satisfies the inequality by testing a point not on the line.

Graphing on the Coordinate Plane

The coordinate plane is a two-dimensional plane formed by the intersection of a horizontal x-axis and a vertical y-axis.
Each point on the coordinate plane is uniquely represented by an ordered pair (x, y), where x is the horizontal coordinate and y is the vertical coordinate.
The origin, (0, 0), is the point where the x-axis and y-axis intersect.
The quadrants are the four regions into which the coordinate plane is divided by the axes. Quadrant I is the upper right; II, upper left; III, lower left; and IV, lower right.
Points in different quadrants have different signs for their x and y coordinates.
Finding the distance between two points on the coordinate plane can be found using the distance formula. The distance formula is derived from the Pythagorean theorem.
The coordinates of any point on the x-axis have a y-coordinate of zero.
The coordinates of any point on the y-axis have an x-coordinate of zero.
Graphing linear equations relies on plotting points and then connecting them to make a straight line.
Using a table of values can help find points on a line.
Linear equations can have infinite solutions.

Description

Test your understanding of linear equations and inequalities with this quiz. Learn about the slope, intercepts, and systems of equations while exploring the differences between linear equations and inequalities. Perfect for reinforcing key concepts in algebra.