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Section 2.3

Section 2.3. Lines. Find slope given two points. m = rise run. Find the slope between (4,-5) and (-6,-1). -1 – -5 -6 – 4 m = -1 + 5 -6 – 4 m = 4 -10 m = -2 5. m =. Forms of writing the equation of a line. Slope-intercept form of a line

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Section 2.3

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  1. Section 2.3 Lines

  2. Find slope given two points m = rise run

  3. Find the slope between(4,-5) and (-6,-1) -1 – -5 -6 – 4 m = -1 + 5 -6 – 4 m = 4 -10 m = -2 5 m =

  4. Forms of writing the equation of a line • Slope-intercept form of a line • y = mx + b (m is slope, b is y intercept) • Standard form of the equation of a line • Ax + By = C • Equation of a horizontal line • y = b • Equation of a vertical line • x = a

  5. Graph the line y= ¼x – 5by graphing y-intercept and slope y-intercept is -5 Slope is ¼

  6. Find the x and y intercepts and graph 2x + y = 5 • Plug in 0 for x • 2(0) + y = 5 • y = 5 • (0,5) This is the y intercept • Plug in 0 for y • 2x + 0 = 5 • x= 2½ • (2½,0)This is the x intercept

  7. Graph y + 3 = 0 Equation can be rewritten as y = -3 Put a point on the y-axis at -3. Plot any other point with a y-value of -3. (-3,-3) is the easiest.

  8. Graph x = 4 Put a point on the x-axis at the 4. Plot any other point (4,4) with an x-value of 4.

  9. Put into Slope-Intercept Form Slope = Y-intercept =

  10. Writing equation of a line • Need two things: • Slope • Y – intercept • Then plug them into y = mx + b Slope = -4 Y – int: (0,-5)

  11. Write the equation of the line with slope m = 2, through the point (1,-1) y = mx + b y = 2x + b -1 = 2(1) + b -1 = 2 + b -3 = b y = 2x – 3

  12. Write the equation of the line Slope = -2 Y-intercept: (0,4) y = mx + b y = -2x + 4

  13. Find slope m = 7-5 3-2 m = 2 1 Write the equation of the line that goes through the points (2,5) and (3,7) y=mx + b y = 2x + b 5 = 2(2) + b 5 = 4 + b 1 = b y = 2x + 1

  14. Write the equation of the line that goes through the points (-2,4) and (3,-1) Find slope m=-1-4 3--2 m=-5 5 m=-1 y = mx + b Y= -1x + b 4 = -1(-2) + b 4 = 2 + b 2 = b y = -1x + 2

  15. Parallel lines have the same slope y = 4x – 7 and y = 4x + 2

  16. Perpendicular Lines have slopes whose product is -1 y = 2x – 7 and y = -½x + 8 2(-½) = -1 Their slopes are opposite reciprocals

  17. Are the lines parallel, perpendicular or neither? y = ¼x + 5 and 2y = -8x – 6 y = -4x – 3 perpendicular

  18. Are the lines parallel, perpendicular or neither? - 3x + y = 5 and 6x - 2y = 6 y = 3x + 5 -2y = -6x + 6 y = 3x – 3 parallel

  19. Write the equation of the line through the point (-2,1) that is parallel to 2y= 4x -6 Y = 2x – 3 y=mx + b y = 2x + b 1 = 2(-2) + b 1 = -4 + b +4 +4 5 = b Y = 2x + 5

  20. Write the equation of the line through the point (2,4) that is perpendicular to y = 4x -6 y=mx + b y = -¼x + b 4 = -¼(2) + b 4 = -½ + b +½ + ½ 4½ = b Y = -¼x + 4½

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