Algebra 2

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Algebra 2

• Section 2-4
• Writing Linear Equations

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What You'll LearnWhy It's Important

• To write an equation of a line in slope-intercept
  form given the slope and one or two points, and
• To write an equation of a line that is parallel
  or perpendicular to the graph of a given equation
• You can use equations to explore relations in
  telecommunications and business

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Slope-Intercept Form of a Linear Equation

• The slope-intercept form of the equation of a
  line is y mx b, where m is the slope and b is
  the y-intercept

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Example 1

• Find the slope-intercept form of an equation of
  the line that has a slope of -? and passes
  through (-6,1).

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Solution Example 1

• Find the slope-intercept form of an equation of
  the line that has a slope of-? and passes
  through (-6,1).
• You know the slope and the x and y values of one
  point on the graph. Substitute for m, x , and y
  in the slope-intercept form.
• ymx b m-?, x -6, y1
• 1(-?)(-6) b
• 1 4 b
• -3 b The y-intercept is -3.
• Replace m and b in the formula ymx b with
  their values
• So, the equation is slope-intercept form is y
  -?x - 3

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Graph of y -?x - 3
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Point-Slope Form of a Linear Equation

• The point-slope form of the equation of a line is
  y y1 m(x x1) where (x1,y1) are the
  coordinates of a point on the line and m is the
  slope of the line.

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Example 2

• Find an equation of the line that passes through
  (3,2) and (5,3)
• Hint you need to find the slope and
  they-interceptSlope Formula ?

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Solution Example 2

• Find an equation of the line that passes through
  (3,2) and (5,3)
• First use the two points given to find the slope
  of the line.
• Then use the point-slope form to write the linear
  equation. y y1 m(x x1) m½,
  x13, y12
• y 2 ½(x - 3) (distribute to get rid of
  parentheses)
• (add 2 to each side to
  isolate y)
• y ½x ½

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Solution Example 2

• Find an equation of the line that passes through
  (3,2) and (5,3)
• I could have used (5,3) as x1 and y1
• Then use the point-slope form to write the linear
  equation. y y1 m(x x1) m½,
  x15, y13
• y 3 ½(x - 5) (distribute to get rid of
  parentheses)
• (add 3 to each side to
  isolate y)
• y ½x ½

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Real Life ApplicationRenting a Car
3 min 4 sec
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Example 3

• With a certain long-distance company, the price
  of a 4-minute long-distance call is 1.70. An
  11-minute call with the same company costs 4.15.
• a. Write a linear equation that describes the
  cost of these telephone calls. Assume that the
  changes increase linearly.
• b. How much would a 20-minute telephone call cost?

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Solution Example 3A

• With a certain long-distance company, the price
  of a 4-minute long-distance call is 1.70. An
  11-minute call with the same company costs 4.15.
• a. Write a linear equation that describes the
  cost of these telephone calls. Assume that the
  changes increase linearly.
• The line passes through the points (4,1.70) and
  (11,4.15). Find the slope of the line.
• Now use the point-slope from to write the linear
  equation. y y1 m(x x1) m0.35,
  x14, y11.70
• y 1.70 0.35(x - 4) (distribute to get rid of
  parentheses)
• y-1.70 0.35x 1.4 (add 1.70 to each side to
  isolate the y)
• y0.35x 0.3

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Solution Example 3b

• With a certain long-distance company, the price
  of a 4-minute long-distance call is 1.70. An
  11-minute call with the same company costs 4.15.
• b. How much would a 20-minute telephone call
  cost?
• y0.35x 0.3
• y0.35(20) 0.3
• y70.3
• y7.30
• A 20-minute call would cost 7.30

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Example 4Integration Geometry

• Write an equation of the line that passes through
  (-9,5) and is perpendicular to the line whose
  equation is y-3x 2

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Solution Example 4Integration Geometry

• Write an equation of the line that passes through
  (-9,5) and is perpendicular to the line whose
  equation is y-3x 2
• The slope of the given line is -3. So the slope
  of the perpendicular line is the opposite
  reciprocal of -3/1 which is 1/3
• You can use either ymx b or y y1 m(x x1)
  
• y mx b m?, x-9, y5
• 5 ?(-9) b
• 5 -3b
• b 8
• y ?x 8

When you graph both lines on a graphing
calculator sometimes you need to zoom in to see
the 90 degree angle
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Special Case

• Write an equation in slope-intercept form that
  satisfies each condition.
• Passes through (6,2) and (6,5)

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Solution Special Case

• Write an equation in slope-intercept form that
  satisfies each condition.
• Passes through (6,2) and (6,5)
• Find the slopeThe slope is undefined, so the
  line is vertical
• Vertical lines cross the x-axis
• At what number does this vertical line pass
  through the x-axis?
• At x 6

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THE END