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1.Given slope (m) and y-intercept (b) create the equation in slope- intercept form. 2. Look at a graph and write an equation of a line in slope- intercept form. 3. Know how to plug into point-slope form. 4. Find the slope between two points. 5. Write an equation of a line that passes through two points. 6. Find an equation of a line that is parallel to an equation given and also given a random point. 7. Find an equation of a line given a slope and a random point. 8. Decide which two lines are parallel. 9. Convert an equation into standard form. 10. Write an equation of a horizontal (y = #) or vertical line (x = #). 11. Decide which two lines are perpendicular. 12. Look at an equation of a line and find the slope of that line.

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Slope-Intercept Form Standard Form Point-Slope Form

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Let’s try one… Given “m” (the slope remember!) = 2 And “b” (the y-intercept) = +9 All you have to do is plug those values into y = mx + b The equation becomes… y = 2x + 9

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Given m = 2/3, b = -12, Write the equation of a line in slope-intercept form. Y = mx + b Y = 2/3x – 12 ************************* One last example… Given m = -5, b = -1 Write the equation of a line in slope-intercept form. Y = mx + b Y = -5x - 1

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GUIDED PRACTICE for Example 1 Write an equation of the line that has the given slope and y- intercept. 1. m = 3, b = 1 y = x + 1 3 ANSWER 2. m = –2, b = –4 y = –2x – 4 ANSWER 3. m = –, b = 3 4 7 2 y = – x + 3 4 7 2 ANSWER

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1) m = 3, b = -14 2) m = -½, b = 4 3) m = -3, b = -7 4) m = 1/2, b = 0 5) m = 2, b = 4 6) m = 0, b = -3 y = 3x - 14 y =-½x + 4 y =-3x - 7 y = ½x y =2x + 4 y = - 3

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Write an equation given the slope and y-intercept Write an equation of the line shown in slope-intercept form. m = ¾ b = (0,-2) y = ¾x - 2

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True False

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a) -4/3 b) -3/4 c) 4/3 d) -1/3

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a) x = -5 b) y = 7 c) x = y d) x + y = 0

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Point-Slope Form Standard Form

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Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2. y – y 1 = m(x – x 1 ) y – 1 = -2(x – 4) Substitute 4 for x 1, 1 for y 1 and -2 for m. Write in slope-intercept form. y – 1 = -2x + 8 Add 1 to both sides y = -2x + 9

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Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7. y – y 1 = m(x – x 1 ) y – 3 = 7[x – (-1)] y – 3 = 7(x + 1) Write in slope-intercept form y – 3 = 7x + 7 y = 7x + 10

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y 2 – y 1 m =m = x 2 – x 1 4--4 = -1-3 8 –4 == –2 y 2 – y 1 = m(x – x 1 ) Use point-slope form. y + 4 = – 2(x – 3) Substitute for m, x 1, and y 1. y + 4 = – 2x + 6 Distributive property Write in slope-intercept form. y = – 2x + 2

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1) (-1, -6) and (2, 6) 2) (0, 5) and (3, 1) 3) (3, 5) and (6, 6) 4) (0, -7) and (4, 25) 5) (-1, 1) and (3, -3)

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GUIDED PRACTICE for Examples 2 and 3 GUIDED PRACTICE 4. Write an equation of the line that passes through (–1, 6) and has a slope of 4. y = 4x + 10 5. Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1. y = 3x – 14 ANSWER

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Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form SOLUTION The line passes through (x 1, y 1 ) = (5,–2) and (x 2, y 2 ) = (2, 10). Find its slope. y 2 – y 1 m =m = x 2 – x 1 10 – (–2) = 2 – 5 12 –3 == –4 y 2 – y 1 = m(x – x 1 ) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x 1, and y 1. y – 10 = – 4x + 8 Distributive property Write in slope-intercept form. y = – 4x + 18

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1) Which of the following equations passes through the points (2, 1) and (5, -2)? a. y = 3/7x + 5b. y = -x + 3 c.y = -x + 2d. y = -1/3x + 3

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a) y = -3x – 3 b) y = -3x + 17 c) y = -3x + 11 d) y = -3x + 5

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y 2 – y 1 m =m = x 2 – x 1 9 – 5 = 1 – -1 4 2 == 2 y – 9 = 2(x – 1) y – 9 = 2x - 2 y = 2x + 7 -2x + y = 7 -2x 2x - y = -7

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y + 5 = ½(x – 4) y + 5 = ½x - 2 y = ½x - 7 -x + 2y = -14 -x x - 2y = 14 2y = x - 14 Multiply everything by 2 to get rid of the fraction

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y – 4 = ⅔ (x – 6) y – 4 = ⅔ x - 4 y = ⅔ x -2x + 3y = 0 -2x 2x - 3y = 0 m = ⅔ 3y = 2x Multiply everything by 3 to get rid of the fraction

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EXAMPLE 2 Write an equation in standard form of the line that passes through (5, 4) and has a slope of –3. y – y 1 = m(x – x 1 ) Use point-slope form. y – 4 = –3(x – 5) Substitute for m, x 1, and y 1. y – 4 = –3x + 15 Distributive property SOLUTION y = –3x + 19 Write in slope-intercept form. 3x + y = 19 +3x

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Parallel vs. Perpendicular Lines

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EXAMPLE 3 b. A line perpendicular to a line with slope m 1 = –4 has a slope of m 2 = – =. Use point-slope form with (x 1, y 1 ) = (–2, 3) 1 4 1 m1m1 y – y 1 = m 2 (x – x 1 ) Use point-slope form. y – 3 = (x – (–2)) 1 4 Substitute for m 2, x 1, and y 1. y – 3 = (x +2) 1 4 Simplify. y – 3 = x + 1 4 1 2 Distributive property Write in slope-intercept form. Write equations of parallel or perpendicular lines

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y = 3 (or any number) Lines that are horizontal have a slope of zero. They have “run” but no “rise”. The rise/run formula for slope always equals zero since rise = o. y = mx + b y = 0x + 3 y = 3 This equation also describes what is happening to the y-coordinates on the line. In this case, they are always 3.

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x = -2 Lines that are vertical have no slope (it does not exist). They have “rise”, but no “run”. The rise/run formula for slope always has a zero denominator and is undefined. These lines are described by what is happening to their x-coordinates. In this example, the x- coordinates are always equal to -2.

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a) x = -5 b) y = 7 c) x = y d) x + y = 0

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a) Y = 2x + 3 b) Y – 2x = 4 c) 2x – y = 8 d) Y = -2x + 1

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