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2.2 Linear Equations

2.2 Linear Equations. Linear Equations. Linear Function : Functions whose graph is a line. Dependent Variable : y is a dependent variable of x because y is the output of x. Independent Variable : x is an independent variable because x is your input values. Slope Dude.

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2.2 Linear Equations

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  1. 2.2 Linear Equations

  2. Linear Equations Linear Function: Functions whose graph is a line. Dependent Variable: y is a dependent variable of x because y is the output of x. Independent Variable: x is an independent variable because x is your input values.

  3. Slope Dude http://www.teachertube.com/viewVideo.php?title=Slope_Dude&video_id=125151

  4. Slope is the rate of vertical change to the horizontal change of a line. • Slope: • Where are two points

  5. Pick two points on the line. Starting with the left most point, count rise and run When counting rise: Up is positive rise Down is negative rise When counting run: Right is positive run Left is negative run

  6. 1) 2) 3) 4)

  7. When finding slope from two points use the formula

  8. Special Cases in Slope Vertical Lines: lines with zero change is the x values have an UNDEFINED slope Horizontal Lines: lines with zero change in the y values and have a ZERO slope

  9. y-intercept form: • x and y are our variables • mis our slope • b is our y-intercept or where the line crosses the y-axis y-intercept RUN RISE Slope

  10. y = (½)x + 3 2) y= -3x 3) y = 5

  11. 1) y = (-1/4)x - 2 2) y = x 3) y = (3/4)x + 1 4) y = -2x + 4

  12. Standard Form: Where A, B, and C are coefficients, and x and y are our variables. (C/B) is our y-intercept (C/A) is our x-intercept y-intercept x-intercept

  13. x – 3y = 6 2) 2x + y =4 3) 5x – 2y =10

  14. 1) x – 2y = -4 2) x + 2y = 0 3) 2x + 3y = 6 4) 2x + y = 1

  15. Point-Slope Form: • Another form of a linear equation is the point-slope form. This form is mainly used for when the y-intercept is not clearly shown on the graph • Where x and y are our variables • m is the slope • And is any point on the line.

  16. y – 3 = (1/2)(x – 2) 2. y + 2 = (-3)(x – 1)

  17. Graph the following: • y – 2 = (-2/3)(x + 1) • y + 3 = (3/2)(x - 2) • y – 1 = (3)(x - 3)

  18. Writing Linear Equations

  19. Y-Intercept Form: • Y and X are our variables • m = slope • b is our y-intercept, or where the line crosses the y-axis

  20. Find the Equation of the line.

  21. Find the Equation of the line.

  22. Find the Equation of the line: A line with slope (4/3) that passes through the point (-3,1).

  23. You Try! Find the Equation of the line: A line with an x-intercept of -3 that passes through the point (1,4).

  24. Special Relationships of Pairs of Lines Equation 1: Equation 2:

  25. Special Relationships of Pairs of Lines Equation 1: Line that passes through (0,3) and (-3,4) Equation 2: Line that passes through (0,-2) and (-3, -1)

  26. Two lines are parallel when they have the same slope. Parallel lines are coplanar lines that do not intersect

  27. Determine if these pairs of lines are parallel. y = (-1/4)x + 2 and y = (-1/2)x + 2 y = 2x + 3 and y – 2 = 2(x + 1) 2x + 4y = 8 and y = (-1/2)x – 2 y – 1 = (1/5)(x – 0) and 1x – 6y = 6

  28. Special Relationships of Pairs of Lines Equation 1: Equation 2:

  29. Special Relationships of Pairs of Lines Equation 1: Line that passes through (0,-1) and (4,-2) Equation 2: Line that passes through (0,-4) and (1, 0)

  30. Two lines are perpendicular when they have the opposite reciprocal slopes. Perpendicular lines are lines that intersect at a right angle.

  31. Determine if these pairs of lines are perpendicular. y = (-2/3)x + 2 and y = (3/2)x + 1 y = 2x + 4 and y – 2 = (1/2)(x + 1) 4x – 2y = 8 and y = (-1/2)x – 2 y – 1 = (1/5)(x – 1) and 1x – 6y = 6

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