Point Slope Form

1
Point Slope Form

• Chapter 2.3

2

• The other format for straight-line equations is
  called the "point-slope" form. For this one, they
  give you a point (x1, y1) and a slope m, and have
  you plug it into this formula
• y - y 1 m (x - x 1 )
• The slope of the line is m
• A known point on the line is (x1, y1).

3
Example

• Find the equation of the straight line that has
  slope m 4 and passes through the point (1,
  6).
• We know m 4, x1 1, and y1 6.  I'll plug
  these values into the point-slope form and we
  get
• y y1 m (x x1)y (6) (4)(x (1))y
  6 4(x 1) This is the answer

4

• Now if we were to distribute and solve for y we
  would have it back in slope intercept form.
  Watch!
• y 6 4(x 1) Answer from previous slide
• y 6 4x 4y 4x 4 6
• y 4x 2 This form should look
  familiar

5
Example 2

• Find the equation of the line that passes through
  the points (2, 4) and (1, 2).
• Then I can use either point as my (x1, y1), along
  with this slope Ive just calculated, and plug in
  to the point-slope form. Using (2, 4) as the
  (x1, y1), I get
• y y1 m (x x1)y (4) ( 2/3)(x (2))y
  4 ( 2/3)(x 2)

6
Function Notation

• Function Notation y f(x) tells you that y is a
  function of x. If there is a rule relating y t ox
  such as y 3x -2 then you can write the equation
  as
• f(x) 3x -2
• This is read as f of x

7
Domain and Range

• The domain of a function is the set of all values
  for which x is defined.
• The range of a function is the set of all values
  for which y is defined.

8
Example

• What is the domain and range of
• f(x) 2x 7?
• Domain and Range are all real numbers
• What if it was applied the following. An online
  video company charges 7 dollars a month plus 2
  dollars per movie. What is the new range and
  domain?
• Domain is x gt 0 Range is x gt 7

9
Homework

• P. 61
• Foundation 1 - 4
• Core 6, 11-19, 21-24
• Challenge 10, 20