graphing systems

Front

What is the solution to a system of equations represented graphically?

Back

The point where the two lines intersect, representing the values of the variables that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are the same in a system of equations?

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines: if slopes are equal and y-intercepts are different, no solution; if slopes are equal and y-intercepts are the same, infinitely many solutions; if slopes are different, one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the slope of a line?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you graph a linear equation?

Back

Identify the y-intercept, use the slope to find another point, and draw a line through the points.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is an example of a system of equations with one solution?

Back

y = 2x + 1 and y = -x + 4 intersect at one point.

Tags

CCSS.8.EE.C.8B