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1.Given slope (m) and y-intercept (b) create the equation in slopeintercept form. 2. Look at a graph and write an equation of a line in slopeintercept form. 3. Know how to plug into point-slope form. y y1 m(x x1) y y1 m 2 4. Find the slope between two points. x 2 x1 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. Slope-Intercept Form Standard Form y mx b m slope of the line b y intercept Ax By C A, B, and C are integers A 0, A must be postive y y1 m x x1 Point-Slope Form m slope of the line x1 , y1 is any point 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 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 GUIDED PRACTICE for Example 1 Write an equation of the line that has the given slope and y-intercept. 1. m = 3, b = 1 ANSWER y=3x+1 2. m = –2 , b = –4 ANSWER y = –2x – 4 3. m=– 3, b = 4 ANSWER 7 3 y=– x+ 4 2 7 2 1) m = 3, b = -14 y = 3x - 14 2) m = -½, b = 4 y =-½x + 4 3) m = -3, b = -7 y =-3x - 7 4) m = 1/2 , b = 0 y = ½x 5) m = 2, b = 4 y =2x + 4 6) m = 0, b = -3 y=-3 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 True False a) b) c) d) -4/3 -3/4 4/3 -1/3 a) b) c) d) x = -5 y=7 x=y x+y=0 Point-Slope Form Standard Form Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2. y – y1 = m(x – x1) y – 1 = -2(x – 4)Substitute 4 for x , 1 for y and -2 for m. 1 Write in slope-intercept form. y – 1 = -2x + 8 Add 1 to both sides y = -2x + 9 1 Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7. y – y1 = m(x – x1) y – 3 = 7[x – (-1)] y – 3 = 7(x + 1) Write in slope-intercept form y – 3 = 7x + 7 y = 7x + 10 4--4 y2 – y1 = m= x2 – x1 -1-3 8 = –4 y2 – y1 = m(x – x1) Use point-slope form. y + 4 = – 2(x – 3) Substitute for m, x1, and y1. y + 4 = – 2x + 6 Distributive property y = – 2x + 2 = –2 Write in slope-intercept form. 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) GUIDED PRACTICE 4. Write an equation of the line that passes through (–1, 6) and has a slope of 4. ANSWER 5. for Examples 2 and 3 y = 4x + 10 Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1. ANSWER y = 3x – 14 Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form SOLUTION The line passes through (x1, y1) = (5,–2) and (x2, y2) = (2, 10). Find its slope. 10 – (–2) y2 – y1 12 = m= = –3 x2 – x1 2 –5 = –4 y2 – y1 = m(x – x1) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x1, and y1. y – 10 = – 4x + 8 Distributive property y = – 4x + 18 Write in slope-intercept form. 1) a. c. Which of the following equations passes through the points (2, 1) and (5, -2)? y = 3/7x + 5 y = -x + 2 b. y = -x + 3 d. y = -1/3x + 3 a) b) c) d) y y y y = = = = -3x -3x -3x -3x –3 + 17 + 11 +5 9–5 y2 – y1 4 = m= = 2 x2 – x1 1 – -1 y – 9 = 2(x – 1) y – 9 = 2x - 2 y = 2x + 7 -2x -2x -2x + y = 7 2x - y = -7 =2 y + 5 = ½(x – 4) y + 5 = ½x - 2 y = ½x - 7 2y = x - 14 -x -x -x + 2y = -14 x - 2y = 14 Multiply everything by 2 to get rid of the fraction m=⅔ y – 4 = ⅔(x – 6) y – 4 = ⅔x - 4 y = ⅔x 3y = 2x -2x Multiply everything by 3 to get rid of the fraction -2x -2x + 3y = 0 2x - 3y = 0 EXAMPLE 2 Write an equation in standard form of the line that passes through (5, 4) and has a slope of –3. SOLUTION y – y1 = m(x – x1) Use point-slope form. y – 4 = –3(x – 5) Substitute for m, x1, and y1. y – 4 = –3x + 15 Distributive property y = –3x + 19 +3x +3x 3x + y = 19 Write in slope-intercept form. Parallel vs. Perpendicular Lines EXAMPLE 3 Write equations of parallel or perpendicular l b. A line perpendicular to a line with slope m1 = –4 has a slope of m21= –1 = . Use point-slope form m1 4 with (x1, y1) = (–2, 3) y – y1 = m2(x – x1) 1 y–3= 4 1 y–3= 4 1 y–3= 4 Use point-slope form. (x – (–2)) Substitute for m2, x1, and y1. (x +2) Simplify. 1 2 x+ 1 7 y x 4 2 Distributive property Write in slope-intercept form. 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. 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 xcoordinates are always equal to -2. a) b) c) d) x = -5 y=7 x=y x+y=0 a) b) c) d) Y = 2x + 3 Y – 2x = 4 2x – y = 8 Y = -2x + 1