Modelling Liner Relations

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Modelling Liner Relations

Equations of lines

y = 0.5 + 3

the Y-Intercept is 3

= 0.5

3 6

m = rise run

calculate the slope, M, of the line using the two points (2,4) and (8,7)

+6 (8,7) +3 (2,4)

the total cost for an ice cream sundae with different numbers of toppings. if X represents the number of toppings and Y represents the total cost in dollars

graph a line using the y-intercept and the slope

= 2 1

slope = rise run

the y-intercept is -3, so plot (0,-3) first. in y = mx + b form, the slope of the line is the coefficient of X, which is 2

y = 2x -3

identify the slope and y-intercept

Identify the slope and the y-intercept of a linear relation involving temperature

The slope of F = 1.8c +32 and F - intercept is +32

the rate of change in the y-values is consistently + 1.8 and when X = 0, Y = 32

the relationship between temperatures in degrees Fahrenheit and degrees Celsius is linear. the equation can be written. y = 1.8x + 32. X is in degrees Celsius and Y is in degrees Fahrenheit 0*c converts to +32*F

the slope of the line is 1.8 and the vertical intercept is +32

F = 1.8c + 32

for the linear relation identify the slope and the y-intercept

Operation's with fractions and Decimals

= 4/3

= 16 divided 4 12 divided 4

16/12

Operation's with integer's

= 13

= 5 + 8

5 - (-8)

Common factors

greatest whole number that divides evenly into both 18 and 21 is 3

factors of 21: 1,3,7 and 21

factors of 18: 1,2,16,9 and 18

18,21

Working with Variables

x = -2

-3x/-3 = 6/-3

-3x = 6

Key terms

run

Rise

y-intercept

Coefficient

Rate Of Change

Slope

Linear Relation

Key Terms

Formula Variable Term

Opposite Operations

Constant Term

Standard Form

Solve A Linear Equation Involving a fraction

k = 12

0.75k = 9 0.75 0.75

0.75k = 9

3k = 9 4

Working With Fractions

the least number that appears in both is 12. 12 is the least common denominator

6: 6,12,24,30,36

4: 4,12,16,20,24

list the multiple's of each denominator

denominator is the least common multiple of the denominations.

denominator is the least common multiple

1/4, 5/6 ( the least common)

rearrange formulas

y - b = mx m m

y - b = x m

divide both sides of the equation by m to isolate x

y - b = mx

y = mx + b, solve for X

y = mx + b subtract b from both sides of the equation

y - b = mx + b - b

Evaluating Expressions

5

8 - 3

4 (2) + 3 (-1)

4x + 3y

Evaluate each expression for x = 2 and y = -1

identify the steps required to solve a multi-step liner equation

or to solve the equation, perform the opposite operations in revers orders

the solution is

X = 25

divide by 2 to find the value of X

50 = 25 2

subtract 10 from the product

60 - 10 = 50

multiply 20 by 3

20 x 3 = 60

2x + 10 = 20 3

divide by 3

the result = 20

multiply x by 2

add 10 to the product

Volume of a gas

810 = 5x 5 5

162 = x

start with 725

subtract 455

multiply by 3

divide by 5

result is 162

810 = 5x

270 = 5x 3

3(270) = 3

(5x/3)

start with X

multiply by 5

Divide by 3

add 455

result is 725

725 = 5x + 455 3

725 - 455 = 5x + 455 - 455 3

y = mx + b

volume of has is 725 cm3

between the volume of a gas in cubic centimeters Y and the temperature in degrees Celsius X

Simplifying Algebraic Expressions

= 2+7r + 4z

= 4 - 2 + 4r +3r - z + 5z

4 + 4r - z + 3r + 5z - 2

Solve a two - step linear equation

X = 2

2x = 4

remove zero pairs

2x - 3 + 3 = 1 + 3

to keep the equation balanced, add 3 to the right side

to isolate the variable term, 2x add 3 to the left side

2x - 3 = 1