solve systems by graphing

Front

What is the solution to a system of equations when two lines intersect?

Back

The solution is the point of intersection of the two lines, which represents 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 when graphing a system of equations?

Back

If two lines are parallel, it means there is no solution to the system of equations, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

If two lines are the same, it means there are infinitely many solutions to the system, 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 equations by graphing?

Back

You can determine the number of solutions by observing the intersection points of the lines: one solution (intersecting), no solution (parallel), or infinitely many solutions (same line).

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the equation y = 2x + 1?

Back

The graph is a straight line with a slope of 2 and a y-intercept of 1.

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

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

How do you graph the equation x = 3?

Back

The graph of x = 3 is a vertical line that crosses the x-axis at the point (3, 0).

Front

What is the solution to the system of equations: y = x + 2 and y = -x + 4?

Back

The solution is the point (1, 3), where the two lines intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Tags

CCSS.8.EE.C.8B