Linear Equations and Inequalities Quiz

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.