Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

GRAPHING from STANDARD FORM

Rewrite the equation in slope­intercept form (y = mx + b), then graph using the y­intercept (b) and the slope (m).

1.) x ­ 2y = 8 * Solve for y!

b = ____m = ____

2.) 6x ­ 3y = 3

b = ____m = ____

3.) 5y = 15x

b = ____m = ____

4.) 2x ­ y = 3

b = ____m = ____

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

GRAPHING LINES from TABLES

If given a table and an equation, follow these steps:1.) Rewrite the equation in slope­intercept form (y = mx + b).2.) Substitute the given inputs/x­values, and solve for the outputs/y­values.3.) Graph using AT LEAST THREE sets of ordered pairs to make sure you have a straight line.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) ­6x + 2y = 10 x y ­1 0 1 2

y = __________

b) 8x ­ 4y = 16 x y ­1 0 1 2

y = __________

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

GRAPHING SPECIAL CASES

Special Cases are graphs with either: * Slope = ZERO; a _________________________________ line * UNDEFINED slope; a _____________________________ line

Examples:

a) x = 4 * Find 4 on the x­axis * Draw a ______________________ line because every number on that line has an x­value of 4.

b) y = ­3 * Find ­3 on the y­axis * Draw a ______________________ line because every number on that line has an y­value of ­3.

c) x = ­1 * Find ­1 on the x­axis * Draw a ______________________ line because every number on that line has an x­value of ­1.

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

WRITING EQUATIONS from GRAPHS

Slope Intercept Form y = ____ x + ____

_______ ______________

Write an equation given the slope and the y­intercept.1) slope = ­5, y­intercept = 2 equation: _______________

2) slope = 1/2 , y­intercept = ­3 equation: _______________

3) slope = 0, y­intercept = 1 equation: _______________

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

4) 5)

Equation: _______________ Equation: _______________

6) 7)

Equation: _______________ Equation: _______________

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

WRITING EQUATIONS from SLOPE & a POINTSteps:1.) Write the slope intercept equation (y = mx + b)2.) Substitute slope in for "m" and the ordered pair in for (x,y)3.) Solve for b (the y­intercept)4.) Substitute the slope (m) and the y­intercept (b) back into the equation5.) Keep the "x" and the "y" in the equation ­ do NOT put numbers in the "x" and the "y" spots.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) Write the equation if the slope is 2 and the line goes through point (2, 3).

b) Slope = 1/2 and (4, ­3)

Unit 5 Smart Notes & TOC.notebook

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February 11, 2019

WRITING EQUATIONS from TWO POINTS

Steps:1.) Use the slope formula m = y2 ­ y1 x2 ­ x1 to calculate the slope.2.) Write the slope intercept equation (y = mx + b).3.) Choose ONE of the ordered pairs.4.) Substitute the ordered pair AND the slope into y = mx + b.5.) Solve for the y­intercept (b).6.) Substitute the slope (m) and y­intercept (b) back into the equation. Do NOT put numbers in for x and y!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) Write the equation of a line which passes through (2, 3) & (4, 5). Slope Solve for b Equation m = y2 ­ y1 (y = mx + b) (y = mx + b) x2 ­ x1

b) (4, ­2) & (2, ­3) Slope Solve for b Equation m = y2 ­ y1 (y = mx + b) (y = mx + b) x2 ­ x1