1. 2.3 Linear Functions

2. A linear function is basically a line!
There are various ways to represent a line/ write its equation
Slope-Intercept Form y = mx + b
Standard Form Ax + By + C = 0
Point-Slope Form y – y1 = m(x – x1)
Reminder: slope =
We should be able to manipulate any of these 3 equations
Note: A lot of these problems come from real world situations
 AKA word problems!  Don’t worry, they are just lines!
m = slope b = y-int
A is whole #
B, C are integers
m = slope
point = (x1, y1)
(doesn’t matter)

3. Ex 1) A teacher believes the number of mistakes made on a simple arithmetic test is a linear function of the room’s temperature. A student makes 8 errors out of 50 questions when it is 68° and 14 errors when it is 76°. What is a linear function that relates the number of errors out of 50 questions to the room temperature. (Temp, errors) (T, E) 2 “points” (68, 8) (76, 14) Find the number of errors a student should make if it is 92°
 26 errors!

4. Here’s another way to write an equation Hmmm, this doesn’t exactly look new! Write a sentence explaining how this equation relates to others we already know Share your sentence with a partner

5. Ex 2) (Using this comboed eqtn) One inch corresponds to 2
Ex 2) (Using this comboed eqtn) One inch corresponds to 2.54 cm and one foot corresponds to cm. Use data to find a linear equation expressing standard measurement as a function of metric measurement. so, x is cm, y is in (2.54, 1) (30.48, 1)
(30.48, 12)
No!

6. Other Notes:
horizontal lines (hit y-axis)
vertical lines (hit x-axis)
parallel lines: have the same slope
perpendicular lines: have slopes that are opposite reciprocals
equation is y = #
equation is x = #
(not a function)

7. Ex 3) Are the two lines parallel, perpendicular, or neither
Ex 3) Are the two lines parallel, perpendicular, or neither? a) 2y + 3x = 3 and y = –1.5x – 0.7
___ _______
2y = –3x + 3
m = –1.5
Parallel
= –1.5
b) 5y – 15x = –4 and 3y + x = 5
5y = 15x – 4
3y = –x + 5
Perpendicular