Half Planes
Boundary Lines
Standard Form
General Form
Factored Form
100

What is a half plane?

The graph of a linear inequality in two variables

100

What is a boundary line determined by an inequality?

It divides the plane into two half planes

100

What is the standard form of a linear equation?

Ax + By = C

100

What is the general form of a linear equation or inequality?

y = ax + b

100

Which equation is in factored form?

y = ax + b       or     y = a(x - c)

y = a(x - c)

200

What ordered pair is generally used to determine the shading of the correct half plane?

(0,0)

200

When is a boundary line dashed?

< or >

200
How is the standard form helpful to students?

Students can substitute 0 for x and then y, to determine the x and y intercepts.  They can then easily graph the equation or boundary line of an inequality.

200
What is the slope in the equation y < 2/5x -7

2/5

200

What is another name for the x-intercept?

the zero of a function

300

In the equation x > 3, which side of the half plane is shaded, left or right?

Right side

300

When is a boundary line in an inequality a solid line?

<=, or >=

300

How can the standard form be turned into the general form?

Isolate y.

300

What is the y intercept of this general form equation?

y = 10x

300

What is the usefulness of the factored form?

It helps determine the x-intercept

400

In the equation 2x + y < y, which half plane is shaded, left or right?

Left

400

Is the boundary line for  y > 5, vertical or horizontal?

horizontal

400
Change this inequality into the general form:

x + y > 5

y > -x + 5

400

With two given equations in general form, how can parallel lines be identified?

The slopes of both equations are the same.

400

How do you check if you have correctly converted the general form of a linear equation into the factored form?

Distribute the slope to the binomial in parentheses.  If  the general form of the equation results, then you have correctly converted it into the factored form.

500

Describe a system of inequalities for which there is no solution.

The inequalities have the same slope and the half planes are shaded in opposite directions.
500

Is the boundary line for x < 12 vertical or horizontal?

Vertical

500

What is the special requirement for the coefficient of x, (represented below by "A") when converting the general form into the standard form?  Ax + By = C

"A" must be a positive integer

500

With two linear equations in general form, how can perpendicular lines be detected without graphing?

Their slopes are negative reciprocals

500

What is the factored form of the following general linear equation:

y = 6x - 48

y = 6(x - 8)

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