Download Algebra 1-2 Unit 2 Objectives and Assignment Guide... UNIT 2: LINEAR FUNCTIONS Essential Questions: 1. How can you represent and describe functions? 2. Can functions describe real-world situations? 3. What does the slope of a line indicate about the line? 4. What information does the equation of a line give you? Objectives: Students will 1. represent functions using tables, equations, and graphs, 2. use function notation, 3. represent arithmetic sequences using function rules, 4. model real-world situations that are continuous and real-world situations that are discrete, 5. find slope using a formula, 6. find slope using a graph, 7. analyze various slopes and describe their meaning, 8. write the equation of a line and give its slope and y-intercept. Topics: 1. Using Graphs to Relate 2 Quantities (F.IF.4) Worksheet 2. Patterns and Linear Functions (F.IF.4 & A.REI.10) Worksheet 3. Graphing a Function Rule & Standard Form (F.IF.5) Ch 3-1 ________________ Ch 3-2 ________________ 4. Rate of Change and Slope (F.IF.6 & F.LE.1b) Ch 3-3 ____________ 5. Direct Variation (A.CED.2) Ch 3-4 _______________ 6. Arithmetic Sequence (F.IF.3 & F.LE.2) Ch 3-5 _______________ 7. Slope Intercept Form (A.CED.2, F.IF.4, F.IF.7a, F.IF.9, F.BF.1, F-LE.2, F-LE.5) Ch 4-1 ________________ Ch 4-2 ________________ 8. Point Slope Form (A.CED.2, F.IF.4, F.IF.7a, F.IF.9, F.BF.1, F-LE.2, F-LE.5) Ch 4-3 ________________ UNIT 2: LINEAR FUNCTIONS (Chapter 3-1 to 3-5, 4-1 to 4-3) Assignment Guide Topic Assignment Graphs w/ 2 Quantities “Using Graphs to Relate 2 Quantities” Worksheet & Vocabulary Worksheet Patterns & Linear Functions “Patterns and Linear Functions” Worksheet & Vocabulary Worksheet QUIZ #1: Ch 3 Graphs of 2 Quantities, Patterns, and Linear Functions Graphing Linear Equations 3-1 pg. 157 #13-19 odd, 20, 23-35 odd, 42, 49 (14 problems) Solving Linear Equations 3-2 pg. 164 #10-15, 22, 23, 38-40, 44 (12 problems) Rate of Change and Slope 3-3 pg. 175 #15-39 odd, 51-53 all (16 problems) Review: Ch 3-1 to 3-3 Review Worksheet QUIZ #2: Ch 3-1 to 3-3 Graphing and Solving Linear Equations & Rate of Change Direct Variation 3-4 pg 183 #1-27 odd, 28 (15 problems) Arithmetic Sequences 3-5 pg. 191 #1-4, 7-11, 13, 15, 17, 32 (13 problems) Review Ch 3-1 to 3-5 Review Worksheet TEST CH 3-1 to 3-5 Linear Functions Graphing in Slope Intercept Form 4-1 pg. Enrichment Rate of Change and Slope & Slope Intercept Form Enrichment Worksheet Writing Equations in Slope Form Form 4-2 pg. Word Problems Wksts Writing Equations in Point Slope Form 4-3 pg. Review Ch 4-1 to 4-3 Unit 2 TEST OR Ch 4-1 to 4-3 Quiz END OF UNIT 2 Due Date Points Showing top 8 worksheets in the category - Unit 2 Linear Function Homework 2 Standard Slope Intercept. Some of the worksheets displayed are Review linear, Work, Math 1, Unit 4 analyze and graph linear equations functions and, Graphing lines in slope intercept, Algebra 1 spencer unit 4 notes inequalities and, Georgia standards of excellence curriculum frameworks, Hw point slope slope intercept work. Once you find your worksheet, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Earlier in this chapter we have expressed linear equations using the standard form Ax + By = C and also y= mx +b. Now we're going to focus on the slope-intercept form y = mx + b. In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. $$y=mx+b$$ Where m is the slope and b is the y-intercept. Example
Graph the equation $$y-2x=1$$ rewrite in slope-intercept form $$y=2x+1$$ Identify the slope and the y-intercept m = 2 and b = 1 Plot the point corresponding to the y-intercept, (0,1) The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2) And once you have your second point you can just draw a line through the two points and extend it in both directions. You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct. Our second point = (1, 3) $$y-2x=1$$ $$3-2\cdot 1=3-2=1$$ Our second point is a solution to the equation i.e. the line we drew is correct. A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation. $$y=mx$$ In a direct variation the nonzero number m is called the constant of variation. You can name a function, f by using the function notion $$f\left ( x \right )=mx+b$$ f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions. A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions. The most basic function in a family of functions is called the parent function. The parent function of all linear functions is $$f\left ( x \right )=x$$ Video lessonGraph y = 3x - 2 |