Parallel and Perpendicular Equations

Hudson graphed the equations y = 2x and y = 2x - 5.

These lines are ​ (a)   because their slopes are ​ (b)   , and their y-intercepts are different.

• parallel
• perpendicular
• equal
• opposite reciprocals
• different, but not opposite reciprocals

Tags

CCSS.HSG.CO.A.1

CCSS.HSG.GPE.B.5

Sadie graphed the equations y = 4 and y = -7.

These lines are ​ (a)   and their slopes equal ​ (b)   .

• parallel
• perpendicular
• opposites
• zero
• undefined

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Gregory graphed the equations y = -3x + 5 and y = 2x - 5.

These lines are ​ ​ (a)   because their slopes are ​ (b)   .

• perpendicular
• intersecting at an angle that is not 90 degrees
• parallel
• different, but not opposite reciprocals
• equal
• opposite reciprocals

Tags

CCSS.HSA.REI.C.6

CCSS.HSG.GPE.B.5

Mabel graphed the equations y = (1/3)x + 2 and y = 3x + 2.

These lines are​ ​ (a)   because their slopes are ​ (b)   .

• perpendicular
• intersecting at an angle that is not 90 degrees
• parallel
• reciprocals, but are not opposites
• equal
• opposites, but not reciprocals

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Put the correct numbers in the spaces to make an equation that is

PARALLEL to y = 3x - 4

and passes through (-2, -1).

y = ​ (a)   x ​ (b)  

• 3
• + 5
• 1/3
• - 3
• + 8
• - 1
• -1/3

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GPE.B.5

Put the correct numbers in the spaces to make an equation that is

PERPENDICULAR to y = 3x - 4

and passes through (6, -8).

y = ​ ​ (a)   x ​ (b)  

• - 6
• 1/3
• - 3
• + 8
• - 4
• -1/3
• - 8

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GPE.B.5

Which pair of numbers are opposite reciprocals?

• -2 and -1/2

• -1/4 and 4

• 2/3 and 3/2

• 7/2 and -3.5

Which TWO equations in standard form are PARALLEL?

(Make sure you choose TWO.)

• 3x - 2y = 14

• 3x - 2y = -6

• 2x - 3y = -6

• 3x + 2y = 14

• 2x + 3y = -14

Answer explanation

The slope from standard form, (Ax + By = C), can be found by taking -A/B from the equation.

Parallel lines have the same slope, so you need two equations where -A/B comes out to the same value.

Tags

CCSS.HSG.GPE.B.5

Which TWO equations in standard form are PERPENDICULAR?

(Make sure you choose TWO.)

• 5x - 2y = 15

• 2x - 2y = -5

• 2x + 5y = 20

• 2x - 5y = 20

• 5x - 5y = -2

Answer explanation

The slope from standard form, (Ax + By = C), can be found by taking -A/B from the equation.

Perpendicular lines have opposite reciprocal slopes, so you need an equation where -A/B has a slope that is positive and an equation that has a slope that is negative AND the reciprocal of the other slope.

Examples of perpendicular slopes:

-4/7 and 7/4

3 and -1/3

"special case": 0 and undefined

Tags

CCSS.HSG.GPE.B.5

Which equation is perpendicular to y = -6?

• y = 2

• y = -6x

• x = -3

• x = -3y

Answer explanation

Slopes of ZERO and UNDEFINED are perpendicular because they intersect at a right angle.

Tags

CCSS.HSG.CO.A.1