Algebra II A – Guided Notes Name ________________________________ 2-2 Guided Notes Period ______________ Linear Equations

Learning Matrix Goal #17: I can locate the information that explains what quantity x and y represents in a real world situation. (Cost, number of things produced, etc.)

Learning Matrix Goal #18: I can determine if negative inputs/outputs make sense in the problem situation (If x represents time, then x cannot be negative).

Learning Matrix Goal #19: I can identify linear equations and functions. Learning Matrix Goal #20: I can find the y-intercept. Learning Matrix Goal #21: I can use the problem situation to explain what the y-intercept means. Learning Matrix Goal #22: I can find the x-intercept.

Learning Matrix Goal #23: I can use the problem situation to explain what the x-intercept means.

How do linear equations relate to time spent studying? Read this on p.63 of your textbook. What does a value of zero for x mean in this situation? What does a negative value for x or for y mean in this situation? Define the following: Linear equation- Linear function- Study Tip When variables other than x and y are used, the letter coming first in the alphabet usually represents the domain variable or horizontal coordinate.

Linear Equations 5x – 3y =7 x = 9 6s = -3t – 15

y =

Not linear equations 7a +4

y = x + xy = 1

y =

Example 1 Identify Linear Functions State whether each function is a linear function. Explain.

a. f(x) = 10 – 5x

b. g(x) = c. h(x,y) = 2xy Your Turn State whether each function is a linear function. Explain.

a. g(x) = 2x-5

b. p(x) =

c. t(x) = 4 + 7x

Example 2 Evaluate a Linear Function Military In August 2000, the Russian submarine Kursk sank to a depth of 350 feet in the Barents Sea. The linear function p (d) = 62.5d + 2117 can be used to find the pressure (lb/f ) at a depth of d feet below the surface of the water.

a. Find the pressure at a depth of 350 feet.

b. The term 2117 in the function represents the atmospheric pressure at the surface of the water. How many times as great is the pressure at a depth of 350 feet as the pressure at the surface?

Your Turn Meteorology The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a given number of degrees Celsius, C.

a. On the Celsius scale, normal body temperature is 37 C. What is normal body temperature in degrees Fahrenheit?

b. There are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equal 1 Celsius degree?

Fill in the blanks: You may find it helpful to remember that if there is no y in the equation, the graph cannot cross the ____-axis. If there is no x in the equation, the graph cannot cross the ____-axis.

Example 4 Use Intercepts to Graph a Line Find the x-intercept and the y-intercept of the graph of 3x – 4y +12 = 0. Then graph the equation. The x intercept is the value of x when y = 0. Likewise, the y-intercept is the value of y when x = 0. Your Turn Find the x-intercept and the y-intercept of the graph of -2x + y -4 = 0. Then graph the equation. ~ 2-2 Linear Equations Guided Notes

~ page 66 #15-24

~ Intercept Notes (link on website - take on separate paper and attach to guided notes) - Learning Matrix Goals #20, 22

~ page 66 #39-49 odd, 48

~ Notes over Linear Equations and Functions textbook page 63 LMG #19

~ Real World Situations and Intercepts Discovery WS - LMG # 17, 18, 21, 23

~ 2-2 Quiz over LMG 17-23