Graphing Linear Systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a solution to a system of linear equations?

Back

The solution is represented by the point where the lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Tags

CCSS.8.EE.B.5

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept is found by setting x = 0 in the equation and solving for y.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be independent?

Back

A system of equations is independent if it has exactly one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the difference between a dependent and an independent system of equations?

Back

A dependent system has infinitely many solutions (the lines overlap), while an independent system has exactly one solution (the lines intersect at one point).

Tags

CCSS.8.EE.C.8B

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.

Front

How can you check the solution of a system of equations graphically?

Back

You can check the solution by graphing both equations and verifying that the point of intersection is the solution.

Tags

CCSS.8.EE.C.8B