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Writing Equations Index Card Activity

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**I. How to Write an Equation of a Line Given m and b**

1. Write down y = mx + b 2. Substitute slope for m and y-intercept for b. 3. Simplify the equation

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**Write the equation of the line given m and b.**

Ex. 1 Slope is -5 and y-intercept is 2 y = -5x + 2 Ex. 2 Slope is -1/2 and y-intercept is -2 y = -½x – 2

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**II. How to Write an Equation of a Line Given a Graph**

Write down y = mx + b Use any 2 “good” points on the graph to find the slope, m. Find the y-intercept on the graph, b. Substitute slope for m and y-int for b into the equation y = mx + b.

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**5. Write the equation of this graph**

m = 6−2 5−0 = 4 5 y = mx + b y = x + b y = x + 2

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**7. Write the equation of Type equation here.this graph**

M = 2 −(−1) 0 −1 = 3 −1 = -3 y = mx + b y = -3x + b y = -3x + 2

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**III. How to Write an Equation of a Line Given m and a point**

Write down y = mx + b. Substitute slope for m and the point (x, y). Solve for b. Substitute m and b back into the equation.

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**Write the equation of the line given m and a point**

Ex 13: m = 2 Point: (2, 3) y = mx + b 3 = 2 (2) + b 3 = 4 + b (subtract 4 from both sides) -1 = b y = 2x – 1

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**3 = 10 + b (subtract 10 from both sides) -7 = b y = -2x – 7**

Write the equation of the line given m and a point Ex 15: m = -2 Point: (-5, 3) y = mx + b 3 = -2 (-5) + b 3 = 10 + b (subtract 10 from both sides) -7 = b y = -2x – 7

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**IV. How to Write an Equation of a Line Given TWO points**

Write down y = mx + b. Use the slope formula to find m. Pick one of the ordered pairs & substitute slope for m and the point (x, y). Solve for b. Substitute m and b into the equation.

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**Equation of a Line - Given 2 points**

Ex: (2, 3) (4, 5) y = mx + b 3 = 1(2) + b 3 = 2 + b (subtract 2 both sides) b = 1 y = x + 1

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**Equation of a Line - Given 2 points**

Ex: (2, 2) (0, 4) y = mx + b y = -1x + b 4 = -1 (0) + b 4 = 0 + b 4 = b y = -x + 4

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**How to Write an Equation of a Line PARALLEL to another and given a point**

1. Given equation should be solved for y (y = mx + b) Write down the slope of that line Substitute m and (x, y) in y = mx + b. Solve for b. Write the equation using m and b.

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**Write a line parallel to the line y = 3x – 5 and passes through the point (-5, -2).**

y = mx + b y = 3x + b -2 = 3 (-5) + b -2 = b (add 15 to each side) 13 = b Work on left side of t-chart, step by step notes on right side y = 3x + 13

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Write a line parallel to the line 2x + y = 3 and passes through the point (-2, 5). Rewrite equation: y = -2x + 3 y = mx + b Y = -2x + b 5 = -2 (-2) + b 5 = 4 + b (subtract 4 from each side) 1 = b Work on left side of t-chart, step by step notes on right side y = -2x + 1

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**1. Given equation should be solved for y (y = mx + b) **

How to Write an Equation of a Line PERPENDICULAR to another and given a point 1. Given equation should be solved for y (y = mx + b) Write down the OPPOSITE RECIPROCAL slope of that line Substitute m and (x, y) in y = mx +b. Solve for b. Write the equation using m and b.

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**Write a line perpendicular to the line y = ½ x – 2 and passes through the point (1, 0).**

Find opposite reciprocal of ½: -2 y = mx + b y = -2x + b 0 = -2 (1) + b 0 = -2 + b (add 2 to each side) 2 = b Work on left side of t-chart, step by step notes on right side y = -2x + 2

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**Write a line perpendicular to the line 2x + 3y = 9 and passes through the point (6, -1).**

Rewrite equation: 3y = -2x (divide both sides by 3) y = − 2 3 x + 3 Find opposite reciprocal of − 2 3 : 3 2 y = mx + b y = x + b -1 = (6) + b -1 = b -1 = 9 + b (subtract 9 from both sides) -10 = b Work on left side of t-chart, step by step notes on right side y = 3/2 x – 10

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