Solutions on a graph

Front

What is a solution of a system of equations?

Back

A solution of a system of equations is a set of values for the variables that makes all the equations true. It is represented as an ordered pair (x, y) on a graph.

Tags

CCSS.8.EE.C.8B

Front

How can you find the solution of a system of linear equations graphically?

Back

To find the solution graphically, plot the equations on a coordinate plane. The point where the lines intersect is the solution to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

If two lines are parallel, it means they have the same slope and will never intersect. Therefore, the system of equations has no solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

If two lines coincide, they lie on top of each other, meaning they have infinitely many solutions as every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the intersection point of two lines?

Back

The intersection point represents the solution to the system of equations, indicating the values of x and y that satisfy both equations.

Tags

CCSS.8.EE.C.8B

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 determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the vertical change (rise) and the horizontal change (run), and divide rise by run.

Tags

CCSS.8.EE.B.5

Front

What is a linear equation?

Back

A linear equation is an equation that forms 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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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

Back

A consistent system of equations has at least one solution, which can be either a single point of intersection or infinitely many solutions.

Tags

CCSS.8.EE.C.8B