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If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

coordinate plane

direct variation

ordered pair

origin

A coordinate system formed by the intersection of a horizonta…

a relationship between two variables in which the data increa…

a pair of numbers used to locate a point on a coordinate grid…

The point (0,0) where the x-axis and the y-axis intersect in…

coordinate plane

A coordinate system formed by the intersection of a horizonta…

direct variation

a relationship between two variables in which the data increa…

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

If x = 27 when y = 6, write the direct variation equation and…

If y = 10 when x = 9, write the direct variation equation and…

If x = 10 when y = 9, write the direct variation equation and…

y = 4.5x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

y = 2/9x; x = 202.5

If x = 27 when y = 6, write the direct variation equation and…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

If x = 27 when y = 6, write the direct variation equation and…

If y = 10 when x = 9, write the direct variation equation and…

If x = 10 when y = 9, write the direct variation equation and…

y = 4.5x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

y = 2/9x; x = 202.5

If x = 27 when y = 6, write the direct variation equation and…

y=8x

y=-5x

y=1/5*x

k=1/8

Find the direct variation equation if y=24 when x=3

Find the direct variation equation if y=-15 when x=3

Find the direct variation equation if y=6 when x=30

Find the constant of variation if x=32 when y=4

y=8x

Find the direct variation equation if y=24 when x=3

y=-5x

Find the direct variation equation if y=-15 when x=3

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

If x = 27 when y = 6, write the direct variation equation and…

If y = 10 when x = 9, write the direct variation equation and…

If x = 10 when y = 9, write the direct variation equation and…

y = 4.5x; x = 10

If y = 27 when x = 6, write the direct variation equation and…

y = 2/9x; x = 202.5

If x = 27 when y = 6, write the direct variation equation and…

direct variation

constant of variation

direct variation formula

solving for k

when two variable quantities have a constant(unchanged) ratio

constant ratio

y=kx... where k is the constant of variation

k=y/x... y=numerator... x=denominator

direct variation

when two variable quantities have a constant(unchanged) ratio

constant of variation

constant ratio

slope

direct variation

the constant of variation for a direct…

parent function

vertical change and horizontal change

mathematical relationship between two variables that can be e…

k is the coefficient of x by dividing each side of y

is the simplest function with these charecteristics

slope

vertical change and horizontal change

direct variation

mathematical relationship between two variables that can be e…

constant of variation

direct variation

rate of change

Which of the following functions is a…

the value of k in a direct variation, y = kx

a function of the form y = kx where k is not zero

how the dependent variable changes with respect to the indepe…

f(x) = 2x

constant of variation

the value of k in a direct variation, y = kx

direct variation

a function of the form y = kx where k is not zero

coordinate plane

direct variation

ordered pair

origin

A coordinate system formed by the intersection of a horizonta…

a relationship between two variables in which the data increa…

a pair of numbers used to locate a point on a coordinate grid…

The point (0,0) where the x-axis and the y-axis intersect in…

coordinate plane

A coordinate system formed by the intersection of a horizonta…

direct variation

a relationship between two variables in which the data increa…

Yes - it passes through the origin

No - it does not pass through the origin

No - there is no constant. (y/x - 4/1,…

yes - there is a constant - 1.5. (y/x…

Is this a direct variation?

Is this a direct variation?

Is this a direct variation?

Is this a direct variation?

Yes - it passes through the origin

Is this a direct variation?

No - it does not pass through the origin

Is this a direct variation?

Formula for Inverse Variation

Formula for Direct Variation

Rules for Inverse Variation

Rules for Direct Variation

xy = k

y = kx

As X goes down Y must go up; Multiply

As X goes up (or down) Y must also go up (or down); Divide

Formula for Inverse Variation

xy = k

Formula for Direct Variation

y = kx

Is this a direct or inverse variation…

Write the equation for the table set b…

Find the missing value

Find the missing value

Suppose y varies directly as x, and y= 16 when x = 8. Find y…

Suppose y varies directly as x, and y = 21 when x = 3. Find x…

Is this a direct or inverse variation…

Write the equation for the table set b…

X axis

Y axis

origin

quandrant

Horizontal number line on a coordinate plane

Vertical number line on a coordinate plane

The point where the two numbers cross each other at the order…

The four regions formed by the X-axis and the Y-axis on a coo…

X axis

Horizontal number line on a coordinate plane

Y axis

Vertical number line on a coordinate plane

Proportion

Ratio

Fraction

Percent

Two ratios that have been set equal to one another, which can…

A comparison between two numbers.

A part of a whole.

A ratio comparing a number to 100.

Proportion

Two ratios that have been set equal to one another, which can…

Ratio

A comparison between two numbers.

The number of goals scored by a soccer…

The pressure of a gas varies directly…

The number of miles a car can be drive…

The number of wrecks at a certain inte…

2/24=4/x... x=48

12.5/250 = x/350... x= 17.5

399/19 = x/8... x= 168

17/833 = 6/x... x= 294

The number of goals scored by a soccer…

2/24=4/x... x=48

The pressure of a gas varies directly…

12.5/250 = x/350... x= 17.5

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 9/2x

y = 2/9x

y = 10/9x

y = 9/10x

If y = 27 when x = 6, write the direct…

y = 9/2x

If x = 27 when y = 6, write the direct…

y = 2/9x

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

Formula for Inverse Variation

Formula for Direct Variation

Rules for Inverse Variation

Rules for Direct Variation

xy = k

y = kx

As X goes down Y must go up; Multiply

As X goes up (or down) Y must also go up (or down); Divide

Formula for Inverse Variation

xy = k

Formula for Direct Variation

y = kx

30

-44

38

-30

Direct Variation: y = 6 when x = 10; find x when y = 18

Direct Variation: y = 22 when x = 8; find y when x = -16

Direct Variation: y = 3.2 when x = 1.6; find y when x = 19

Direct Variation: y = -6 when x = 1.6; find y when x = 8

30

Direct Variation: y = 6 when x = 10; find x when y = 18

-44

Direct Variation: y = 22 when x = 8; find y when x = -16

Direct Variation

Constant of Proportionality

Percent of change

Percent of increase

A linear relationship between 2 variables (y = k/x; k cannot…

The constant k in direct variation

The amount stated as a percent that a number increases or dec…

A percent change describing an increase in quantity

Direct Variation

A linear relationship between 2 variables (y = k/x; k cannot…

Constant of Proportionality

The constant k in direct variation

If y = 27 when x = 6, write the direct…

If x = 27 when y = 6, write the direct…

If y = 10 when x = 9, write the direct…

If x = 10 when y = 9, write the direct…

y = 4.5x; x = 10

y = 2/9x; x = 202.5

y = 10/9x; x = 8.1

y = 9/10x; x = 10

If y = 27 when x = 6, write the direct…

y = 4.5x; x = 10

If x = 27 when y = 6, write the direct…

y = 2/9x; x = 202.5

domain

direct variation

discrete graph

continuous graph

The possible values for the input of a relation or function.

A linear function defined by an equation in the form y = kx,…

A graph composed of isolated points.

A graph that is unbroken.

domain

The possible values for the input of a relation or function.

direct variation

A linear function defined by an equation in the form y = kx,…

domain

direct variation

constant of variation

discrete graph

The possible values for the input of a relation or function

A linear function defined by an equation in the form y = kx,…

The nonzero constant k in the function y = kx

A graph composed of isolated points

domain

The possible values for the input of a relation or function

direct variation

A linear function defined by an equation in the form y = kx,…

If y varies directly with x, find the…

If y varies directly with x, find the…

If y varies inversely with x, find the…

If y varies jointly with x and z, find…

y = 4.5x; x = 10

y = (2/9)x; x = 202.5

y = (3800)/x; y = 50

y = (3/4)xz; y = 36

If y varies directly with x, find the…

y = 4.5x; x = 10

If y varies directly with x, find the…

y = (2/9)x; x = 202.5

Direct Variation

Inverse Variation

Real world situations

Suppose that x and y vary inversely an…

linear function where y=0. ... y=kx ... k- constant of variation

y= k/x or k= yx... k- constant of variation

1st quadrant. ... Rate is the dependent variable, or x. ... Time is…

Step 1: y= k/x ... Step 2: -5= k/3 ... Step 3: k- -15... Step 4: Answe…

Direct Variation

linear function where y=0. ... y=kx ... k- constant of variation

Inverse Variation

y= k/x or k= yx... k- constant of variation