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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.7.EE.B.4A

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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.

Tags

CCSS.HSA.REI.D.12

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.

Front

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6