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Unit 2.2

Unit 2.2. Linear Representation and Equations of Lines. Linear Representations. Linear Data can be represented in a variety of ways: x-y tables Graphs Equations Verbal representation. Slope-Intercept Form of a Line. y = mx + b. Y-intercept of line. Slope of line.

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Unit 2.2

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  1. Unit 2.2 Linear Representation and Equations of Lines

  2. Linear Representations Linear Data can be represented in a variety of ways: • x-y tables • Graphs • Equations • Verbal representation

  3. Slope-Intercept Form of a Line y = mx + b Y-intercept of line Slope of line x and y are points (x,y) on the line

  4. Practice Problems Identify the slope (m) and y-intercept (b) of the following lines: • y = ½ x – 4 • y = -3x + 5 • y = 6 – 2x • y = -2/3x + 10 5. y = -8 + .5x

  5. Writing Linear Equation from Slope and y-intercept • If we know the slope (m) and y-intercept (b), we can write the equation of a line. Examples: m = ¾ , b=-6 Equation: y = ¾ x – 6 m = -2, b = 3 Equation: y = -2x + 3 m = 0, b = 5 Equation: y = (0)x + 5 or y = 5

  6. Practice Problems • Write the equations for the following lines: 1. m = 3, b = -4 2. m = -1/2, b=2 3. m = 6, b = 0 4. m = 2/5, b = -2 5. m = 9/5, b = 32

  7. Write the equation of the line in slope-intercept form for the following graph: m = b = Equation:

  8. Writing Equation from the slope and one point If we know the slope of a line and one point on the line, we can find the y-intercept by doing the following: • Replace m with the slope given in the problem • Use the point we know to replace x and y • Solve for b

  9. Example 1: • Find the equation of the line with a slope of 2 that passes through point (1, 6). • m = 2, x = 1, y = 6 Use the general equation: y = mx + b to find b 6 = 2(1) + b 6 = 2 + b 4 = b Equation of line: y = 2x + 4

  10. Example 2: • Find the equation of the line with a slope of ½ that passes through (4, 8). m = ½ , x = 4, y = 8 y = mx + b 8 = ½(4) + b 8 = 2 + b 6 = b Equation of line: y = ½ x + 6

  11. Practice Problems • Write the equation of the line with the following information: 1. m = -3, contains (1, -12) 2. m = 4, contains (-1, 6) 3. m = -1, contains (0, 3) 4. m = 2/3, contains (6, 9)

  12. Writing Equation from Two Points • We can also write the equation if we know two points on the line: • Find the slope of the line passing through the two points (this is m) • Find the y-intercept by solving for b using the slope and one point on the line • Put m and b into the general equation y = mx + b

  13. Example: • Find the equation of the line passing through (1,4) and (2,2). 1. Find slope: m = = -2 2. Find b: y = mx + b m = -2, x = 1, y = 4 y = mx + b 4 = -2(1) + b 4 = -2 + b 6 = b 3. Equation: y = -2x + 6

  14. Practice Problem • Find the equation of the line passing through (-2,5) and ( 1,2) m = b = Equation:

  15. Example 1: Joe puts $50 in a savings account and saves $15 a week. Table EquationGraph Week Money

  16. Example 2: Cost of fixing a furnace Table: Equation:Graph: Hours Cost 0 $50 1 $75 2 $100 3 $125 4 $150 Verbal:

  17. Table Equation X | Y Example 3:

  18. Standard Form of a Line • The standard form of a line is ax + by = c where a, b, are integers, c is real number and x and y are points on the line • The standard form of a line is often used to find x- and y-intercepts.

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