Graphing Systems of Equations in Slope-Intercept Form

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b).

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (0, b) and then use the slope (rise/run) to find another point.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point, which is the solution (x, y).

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect, indicating there is no point (x, y) that satisfies both equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines coincide, or are the same line, resulting in an infinite number of intersection points.

Tags

CCSS.8.EE.C.8A

Front

How can you check if a point is a solution to a system of equations?

Back

Substitute the (x, y) coordinates into both equations; if both are true, it is a solution.

Front

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

Back

The solution is represented by the point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B