Writing & Solving Linear Functions, Equations, & Inequalities

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean for a solution to be a feasible solution in a linear inequality?

Back

A feasible solution in a linear inequality is a solution that satisfies the inequality and lies within the feasible region defined by the inequality.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation, plot them on a coordinate plane, and draw a straight line through the points.

Front

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

Back

A linear equation shows equality (e.g., y = 2x + 3), while a linear inequality shows a range of values (e.g., y < 2x + 3) and represents a region on a graph.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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How do you find the intersection of two linear equations?

Back

To find the intersection of two linear equations, solve the system of equations simultaneously using substitution or elimination methods.