Presentation on theme: "2.3 Linear Functions. A linear function is basically a line! There are various ways to represent a line/ write its equation Slope-Intercept Form y = mx."— Presentation transcript:
2.3 Linear Functions
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 – y 1 = m(x – x 1 ) 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, B, C are whole #s m = slope point = (x 1, y 1 ) (doesn’t matter)
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!
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
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!
Other Notes: - horizontal lines (hit y-axis) - vertical lines (hit x-axis) - parallel lines: have the same slope - perpendicular lines: have slopes that are negative reciprocals equation is y = # equation is x = # (not a function)
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 = –1.5 ___ _______ 2 2 Parallel b) 5y – 15x = –4 and 3y + x = 5 5y = 15x – 4 3y = –x + 5 Perpendicular