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Point Slope Form

- Chapter 2.3

- 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).

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

- 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

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)

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

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.

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

Homework

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

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