Solutions on a graph

Front

What is a solution to a system of linear equations?

Back

A solution is a point where the graphs of the equations intersect, representing values that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8A

Front

How can you estimate the solution of a system of linear equations from a graph?

Back

By identifying the point where the two lines intersect on the graph.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines on a graph are parallel?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines on a graph coincide?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the coordinates (x, y) in a solution?

Back

They represent the values of the variables that satisfy the equations in the system.

Tags

CCSS.HSA.REI.C.9

Front

If the solution to a system of equations is (3, 0), what does this indicate?

Back

It indicates that when x = 3 and y = 0, both equations in the system are satisfied.

Tags

CCSS.HSA.REI.C.9

Front

What is the graphical representation of the equation y = mx + b?

Back

It is a straight line where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

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

Back

The y-intercept is the point where the line crosses the y-axis (where x = 0).

Front

What is the slope of a line?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does it mean if a system of equations has no solution?

Back

It means the lines representing the equations are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A