5.3 Writing Linear Equations Given Two Points

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5.3 Writing Linear Equations Given Two Points
Objective Write an equation of a line given two
points on the line.

• Type 1 (5.1)
• slope (m)
• y intercept (b)
• Type 2 (5.2)
• slope (m)
• y intercept (b)
• Type 3 (5.3)
• slope (m)
• y intercept (b)

???
???
???
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Writing Equations Type 3

• Ex. 1 Write an equation of the line that goes
  through the points (-2, 1) and (4, 2).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• We need both!! This is a Type 3 problem.
• First, when two points are given, the first thing
  in your mind is to calculate the slope! Plug the
  points into the slope formula.

???
???
or
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Writing Equations Type 3

• Ex. 1 Write an equation of the line that goes
  through the points (-2, 1) and (4, 2).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• Its now a Type 2 problem. Pick one of the
  ordered pairs to plug into the equation. Which
  one looks easiest to use?
• Im using (4, 2) because both numbers are
  positive.
• 2 (4) b

???
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Writing Equations Type 3
2 (4) b Solve the equation for b 2
b To write an equation, you
need two things slope m y
intercept b
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Writing Equations Type 3

• Ex. 2 Write an equation of the line that goes
  through the points (2, 5) and (1, -2).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• We need both!! This is a Type 3 problem.
• First, when two points are given, the first thing
  in your mind is to calculate the slope! Plug the
  points into the slope formula.

???
???
or
6
Writing Equations Type 3

• Ex. 2 Write an equation of the line that goes
  through the points (2, 5) and (1, -2).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• Its now a Type 2 problem. Pick one of the
  ordered pairs to plug into the equation. Which
  one looks easiest to use?
• Im using (2, 5) because both numbers are
  positive.
• 5 (2) b

???
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Writing Equations Type 3
5 (2) b Solve the equation for b 5
b To write an equation, you
need two things slope m y
intercept b
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Write an equation of the line that goes through
the points (0, 1) and (1, 4).

1. y 3x 4
2. y 3x 1
3. y -3x 4
4. y -3x 1

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Writing Equations Type 3

• Ex. 3 Write an equation of the line that goes
  through the points (-1, 6) and (4, 9).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• We need both!! This is a Type 3 problem.
• First, when two points are given, the first thing
  in your mind is to calculate the slope! Plug the
  points into the slope formula.

???
???
or
10
Writing Equations Type 3

• Ex. 3 Write an equation of the line that goes
  through the points (-1, 6) and (4, 9).
• To write an equation, you need two things
• slope (m)
• y intercept (b)
• Its now a Type 2 problem. Pick one of the
  ordered pairs to plug into the equation. Which
  one looks easiest to use?
• Im using (4, 2) because both numbers are
  positive.
• 6 (-1) b

???
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Writing Equations Type 3
6 (-1) b Solve the equation for b 6
b To write an equation, you
need two things slope m y
intercept b
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Write an equation of the line that goes through
the points (-2, 1) and (-3, 3).

1. y 2x 5
2. y 2x 3
3. y -2x 5
4. y -2x 3

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Writing Equations Type 3

• Sometimes, you are given a graph, such as
• How can you write out the
• equation?
• To write an equation, you need
• two things
• slope (m)
• y intercept (b)
• We need both!! First, we pick up two nice
  points. Second, you have to find the slope. Plug
  the points into the slope formula or simply use
  rise over run.

(-6, 1)
(-4, -3)
???
???
or
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Writing Equations Type 3

• To write an equation, you need two things
• slope (m)
• y intercept (b)
• Its now a Type 2 problem.
• Pick one of the ordered pairs
• to plug into the equation.
• Which one looks easiest to use? Im using (-6,
  1)
• 1 (-6) b

???
(-6, 1)
(-4, -3)
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Writing Equations Type 3
1 (-6) b Solve the equation for b
1 b To write an equation, you
need two things slope m y
intercept b
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Writing Equations Type 3

• You Try This!!
• Write the equation for the given graph
• To write an equation, you need
• two things
• slope (m)
• y intercept (b)
• We need both!! First, we pick up
• two nice points. Second, you have to find the
• slope. Plug the points into the slope formula or
• simply use rise over run.

(-3, 1)
???
???
(2, -2)
or
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Writing Equations Type 3

• To write an equation, you need two things
• slope (m)
• y intercept (b)
• Its now a Type 2 problem.
• Pick one of the ordered pairs
• to plug into the equation.
• Which one looks easiest to use? Im using (-3,
  1)
• 1 (-3) b

???
(-3, 1)
(2, -2)
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Writing Equations Type 3
1 (-3) b Solve the equation for b
1 b To write an equation,
you need two things slope m
y intercept b
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Writing Equations Type 3
To find the slope and y-intercept of an equation,
write the equation in slope-intercept form y
mx b.

• Ex. 4 Find the slope and y-intercept.
• 1) y 3x 7
• y mx b
• m 3, b -7

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Writing Equations Type 3
Find the slope and y-intercept.

• 2) y x
• y mx b
• y x 0
• 3) y 5
• y mx b
• y 0x 5

m b 0
m 0 b 5
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Writing Equations Type 3

• When two lines are perpendicular, their slopes
  are opposite reciprocal.
• Ex. 5. Check the two lines are perpendicular.
• y 3x 4 and y -3x -6
• and
• and

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Writing Equations Type 3

• When two lines are parallel, their slopes are
  equal.
• When two lines are perpendicular, their slopes
  are opposite reciprocal.
• Ex. 6. Write an equation of a line through (6,
  1) that is
• parallel to line y 2x 5
• perpendicular to line y 3x 2

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Writing Equations Type 3

• Ex. 6. Write an equation of a line through (6,
  -1) that is
• parallel to line y 2x 5
• To write an equation, you need m and b.
• When two lines are parallel, their slopes are
  equal. The slope of the other line is 2. So m
  2.
• You are also given a point. You should be able
  to find the y-intercept b. (Type 2 problem)
• y mx b
• 1 2(6) b

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Writing Equations Type 3

• Ex. 6. Write an equation of a line through (6,
  -1) that is
• parallel to line y 2x 5
• 1 2(6) b
• 1 12 b
• 12 12
• 11 b
• So the equation of the line is
• y 2x 11

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Writing Equations Type 3
Ex. 6. Write an equation of a line through (6,
-1) that is (2) perpendicular to line y 3x
2 To write an equation, you need m and b.
When two lines are perpendicular, their slopes
are opposite reciprocal. The slope of the other
line is 3. So m . You are also given a
point. You should be able to find the
y-intercept b. (Type 2 problem) y m x
b 1 (6) b
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Writing Equations Type 3

• Ex. 6. Write an equation of a line through (6,
  -1) that is
• parallel to line y 2x 5
• 1 (6) b
• 1 2 b
• 2 2
• 1 b
• So the equation of the line is

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• Summary
• In the Type 3 problem, neither slope nor
  y-intercept is directly provided. Only two
  points are given.
• When you are given two points, the first thing in
  your mind is to find the slope by using the slope
  formula.
• After you find out the slope, the Type 3 problem
  becomes to a Type 2 problem. Please see the top
  box on P. 286.
• When you are given a graph of line, just find two
  grid(latice) points. Then follow the step 2 and
  step 3 above.

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• Summary
• 5. When the two lines are parallel, their slopes
  are equal.
• 6. When the two lines are perpendicular, their
  slopes are OPPOSITE RECIPROCAL.

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Assignment P. 288 s 6 34 (even), 45 47