Unit 2: Linear Functions In-Class Notes and Problems Objective #0: Ordered Pairs and Graphing on a Coordinate Plane

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1 Algebra 1-Ms. Martin Name Unit 2: Linear Functions In-Class Notes and Problems Objective #0: Ordered Pairs and Graphing on a Coordinate Plane 1) Tell what point is located at each ordered pair. (6, 6) (1, - 6) (- 4, - 6) (- 7, 6) (- 3, 8) (8, 4) (6, 7) (5, 8) 2) Write the ordered pair for each given point. N L R I S P H Z 3) Plot the following points on the coordinate grid. Write the letter next to each point. X (6, - 9) O (2, 7) C (9, - 3) U (0, 2) D (- 2, 3) B (8, 2) Y (- 9, - 6) W (- 1, 6)

2 Objective #1: Graphing Functions Objective 1 Graphing Functions Notes: A graph of an equation represents all solutions (x, y) that make the equation true. Here are the steps to graph an equation with an x and a y: 1. Choose values for x and write them in a table. a. It s often a good idea to choose -2, -1, 0, 1, and Plug each value into the equation for x and see what y-value makes the equation true. This will give you ordered pairs (x, y). 3. Graph the ordered pairs. Then, connect the points with a line or curve. 1) Create a table and graph for each equation. Show your work. y = 2x x plug in and simplify- OPTIONAL y (x, y)

3 2) y = x + 4 x plug in and simplify - OPTIONAL y (x, y) 3) y = x 2 x plug in and simplify y (x, y) 4) y = 4 Hint: it doesn t matter what x is! y will always be 4! x plug in and simplify- OPTIONAL y (x, y)

4 5) y = 4x 3 x plug in and simplify y (x, y) 6) y = 1 2 x 1 x plug in and simplify y (x, y) 7) y = 2x +1 x plug in and simplify y (x, y)

5 Objective #2: Function Notation Notes: 1) Explain the difference between ( 4) 2 and 4 2 For 2 10: If f(x) = 2x 4 and g(x) = x 2 4x, find each value. Show your work. 2) f(4) 3) g(2) 4) f(-5) 5) g(-3) 6) f(0) 7) g(0) 8) f 1 2 9) g(4) 10) g(-4)

6 11) Create a table and graph for each function. Put all 3 graphs on the same grid. Show your work. f(x) = -2x 1 g(x) = -2x + 4 h(x) = 1 2 x x plug in f(x) x plug in g(x) x plug in h(x)

7 Objective #3: Standard Form and Graphing using the Intercept Method The x- intercept is the place (or places) where a graph crosses the x- axis. To find the x- intercept, replace the y with zero and solve for x. The y- intercept is the place (or places) where a graph crosses the y- axis. To find the y- intercept, replace the x with zero and solve for y. 1) Use the graph to find the x-intercept and the y-intercept for the lines shown below.

8 For #2-7: Graph each linear function by finding the x-intercept and the y-intercept. Show work. 2) 6x = -3y+ 6 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, ) 3) 2x = 2y + 6 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, ) 4) 2x + y = -2 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, )

9 5) 3x 6y = -6 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, ) 6) -2x + 4y = -8 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, ) 7) y = 3x - 1 Find the x-intercept: Find the y-intercept Graph the line: x-intercept: (, ) y-intercept: (, )

10 Objective #4: Slope of a Line For #1-6, find the slope of the line that passes through each pair of points. 1) (4, 9) and (1, 6) 2) (-4, -1) and (-2, -5) 3) (-4, -1) and (-4, -5) 4) (2, 1) and (8, 9) 5) (14, -8) and (7, -6) 6) (4, -3) and (8, -3)

11 7) Find the slope of the lines shown below. 8) The graph below shows the annual coal exports from U.S. mines in millions of tons. 9) The table shows the population density for the state of Texas in various years. Find the average annual rate of change in the population density from 2000 to 2009.

12 Objective #5: Point-slope form of a line For #1-7, write an equation in point-slope form for the line that passes through the given point with the given slope. 1) (2, 1), m = 4 2) (-7, 2), m = 6 3) (8, 3), m = 1 4) (-6, 7), m = 0 5) (4, 9), m = ¾ 6) (0, 5), m = -½ 7) Write an equation in point-slope form for a horizontal line that passes through the point (4, -2)

13 For #8-10, write two different equations in point-slope form for the lines shown. 8) 9) 10) 11) 12) 13) For #14-19 graph the lines described below WITHOUT using a table 14) y = 3(x 1) ) y = -1(x + 2) 3 16) y = ½ (x 4) ) y = (x + 1) 18) y = 3(x 2) 19) y = -2x

14 Objective 6 Slope-Intercept Form Notes: For #1-6, write an equation in slope-intercept form for the line that passes through the given point with the given slope. 1) (0, 1), m = 4 2) (0, 2), m = 6 3) (0, -3), m = 1 4) (0, -7), m = 0 5) (0, 9), m = ¾ 6) (0, -5), m = -½ 7) Write an equation in point-slope form for a horizontal line that passes through the point (0, -2)

15 For #8-13, write the equation of the line shown in slope-intercept form. 8) 9) 10) 11) 12) 13) For #14-19, create a graph for the line given in slope-intercept form. 14) y = 2x ) y = -3x ) y = -x ) y = x 18) y = - ½ x ) y = x + 4

16 Objective 7 Writing an equation of a line when given 2 points Write an equation of the line that goes through the two points given in point-slope form AND in slopeintercept form. 1) Point- slope form: Slope- intercept form: ) Point- slope form: Slope- intercept form:

17 3) Point- slope form: Slope- intercept form: ) (-1, 6) and (7, -10) find slope: point-slope form: slope-intercept form: ) (0, 2) and (1, 7) find slope: point-slope form: slope-intercept form: ) (6, -25) and (-1, 3) find slope: point-slope form: slope-intercept form: ) (-2, -1) and (2, 11) find slope: point-slope form: slope-intercept form:

18 8) (10, -1) and (4, 2) find slope: point-slope form: slope-intercept form: ) (-14, -2) and (7, 7) find slope: point-slope form: slope-intercept form: ) (4, 0) and (0, 2) find slope: point-slope form: slope-intercept form: ) (-3, 0) and (0, 5) find slope: point-slope form: slope-intercept form: ) (0, 16) and (-10, 0) find slope: point-slope form: slope-intercept form:

19 Objective 8 Converting between different forms of a line Notes: Convert the following functions into STANDARD FORM. Then, graph them using the intercept method. Graph all three lines on the same grid. 1) y = 2x 6 Standard form: 2) y = -4x + 4 Standard form: 3) y = 2(x 2) + 8 Standard form:

20 Convert the following functions into SLOPE-INTERCEPT FORM. Then, graph them using the slope and the y-intercept. (y = mx + b) Graph all three lines on the same grid. 4) 2x 4y = 4 Slope-intercept form: 5) 6x 6y = -6 Slope-intercept form: 6) 2x + 3y = 6 Slope-intercept form: