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Name:______________________

1. Use the equation y = -1.5x - 3 to complete the table below and plot the values on to the coordinate grid below.

X | -8 | -6 | -4 | -2 | 0 | 2 | 4 |

Y | 9 | 6 | 3 | 0 | -3 | -6 | -9 |

2. (a) Plot the values from the table on to the coordinate grid below.

X | -6 | -4 | -2 | 0 | 2 | 4 | 6 | 8 |

Y | 11 | 9 | 7 | 5 | 3 | 1 | -1 | -3 |

2. (b) Write the linear equation that defines the relationship between the X and Y values in the form y = mx + b. y = -x + 5

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3. Determine the linear equation in slope intercept form (y = mx + b) based on the tables of values below. (the first one is done for you)

x | 0 | 1 | 2 | 3 | 4 | y = 2x + 5 |

y | 5 | 7 | 9 | 11 | 13 |

Find the value of b: what is the value of y when x = 0? b = 5,

Then

- Subtract 5 from any other y-value. e.g. 11 - 5 = 6.
- What must the corresponding x-value, 3 be multiplied by to equal 6? m = 2
- Repeat as a check with another y-value. e.g. 7 - 5 = 2. Corresponding x-value1 be multiplied by to equal 2? m = 2

Or,

- Pick any other point e.g. (2,9)
- Substitute 2 and 9 for x and y in equation y = mx + 5
- 9 = 2m + 5
- 9 (- 5) = 2m + 5 (- 5)
- 4 = 2m
- m = 2

y = 2x + 5

x | 0 | 1 | 2 | 3 | 4 | y = 3x + 2 |

y | 2 | 5 | 8 | 11 | 14 |

x | -6 | -4 | -2 | 0 | 2 | 4 | y = 1x + 4 |

y | -2 | 0 | 2 | 4 | 6 | 8 |

x | 0 | 1 | 2 | 3 | 4 | 5 | y = -1x + 7 |

y | 7 | 6 | 5 | 4 | 3 | 2 |

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The various resources listed below are aligned to the same standard, (8EE06) taken from the CCSM (Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

*Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. *

- Equation of a Line - Determining & Plotting (4 Pages)
- Calculating the Slope of a Line (2 Pages)
- Converting to Slope Intercept Form (2 Pages)

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

*Understand the connections between proportional relationships, lines, and linear equations*

- Graphing Proportional Relationships (From Example/Guidance)
- Graphing Proportional Relationships (2 Pages) (From Worksheet)
- Calculating & Plotting Coordinates - from linear equations e.g. y = 2x - 6 ( 9 of 10) (From Worksheet)
- Calculating & Plotting Coordinates - from linear equations e.g. y = 2x - 6 ( 10 of 10) (From Worksheet)