# 2.2: Find Slope & Rate of Change 2.3: Graph Equations of Lines Find Slope & Rate of Change Graph Equations of Lines 1. 2. 3. 4. Objectives: To find the slope of a line given 2 points To classify a line based on its slope To find the slope of parallel and perpendicular lines

To graph the equation of a line using slope-intercept and standard form of a line Vocabulary Slope Rate of Change Parallel Perpendicular

Parent Function Intercepts Slope-Intercept Form Standard Form Objective 1 e

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Slope Rate of Change A rate of change is how much one quantity changes (on average) relative to another. Slope can be used to represent an average rate of change. For slope, we measure how changes relative to .

Exercise 1 Describe some real-world rates of change. Practical Slope The slope or pitch of a roof is quite a useful measurement. How do you think a contractor would measure the slope or pitch of a roof?

Pitch of a Roof The slope or pitch of a roof is defined as the number of vertical inches of rise for every 12 inches of horizontal run. Slope Definition The slope m of a nonvertical line is the ratio of vertical

change (the ryse) to the horizontal change (the run). ryse ryse Exercise 2 Regulations state that a handicap ramp must not exceed one inch of rise for every linear foot of

run. If the maximum rise of a handicap ramp is 2.5 feet, what is the longest horizontal length of any handicap ramp? Exercise 3 Find the slope of the line passing through the points (4, 5) and (6, 2). Exercise 4 Find the value of k such that the line passing

through the points (4, 2k) and (k, 5) has slope 1. Objective 2 You will be able use slope to be able to tell what kind of line you have The Slope Game The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical. m>0

m<0 m=0 m = undef Insert Picture Insert Picture

Insert Picture Insert Picture As the absolute value of the slope of a line increases, --?--. the line gets steeper. Exercise 5

Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. 1. (1, 6); (8, 1) 2. (4, 3); (7, 1) 3. (5, 3); (5, 1) 4. (9, 2); (9, 2) You will be able to find the slopes of parallel and perpendicular lines Objective 3

Parallel and Perpendicular Two lines are parallel lines iff they are coplanar and never intersect. Two lines are perpendicular lines iff they intersect to

form a right angle. Parallel and Perpendicular Two lines are parallel lines iff they have the same slope. Two lines are perpendicular lines iff their slopes are negative reciprocals.

Exercise 6 Tell whether the pair of lines are parallel, perpendicular, or neither 1. Line 1: through (-2, 1) and (0, -5) Line 2: through (0, 1) and (-3, 10) 2. Line 1: through (-2, 2) and (0, -1) Line 2: through (-4, -1) and (2, 3) Exercise 7 1. If two distinct lines are parallel, what do you know about their y-intercepts? 2. If one of two perpendicular lines has a

slope of 1/a and a < 0, is the slope of the other line positive or negative? Obj ect i ve 4 e th ph pea gr slo rm

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u t t Yo qua cep e te r in Parent Functions Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function.

Family of Linear Functions Linear Parent Function Parent Functions Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of Quadratic Functions Quadratic Parent Function

Parent Functions Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of Functions Parent Function A group of functions that share common characteristics

Simplest member of the family Parent Functions Linear parent function: or All other linear functions can be formed with transformations on the parent function.

Intercepts 6 The -intercept of a graph is where it intersects the -axis. 4 ( ,0 ) ( 0, )

The -intercept of a graph is where it intersects the -axis. y-intercept 2 -5 x-intercept

5 -2 Click me! Slope-Intercept Slope-Intercept Form of a Line: If the graph of a line has slope and a -intercept of (0, ), then the equation of the line can be

written in the form Slope intercept Slope-Intercept To graph an equation in slope-intercept form: 2. Plot Solve 1. for

Draw 4. line Use to plot 3. more points Exercise 8a Without your graphing calculator, graph each of the following:

1. 2. Exercise 8b Without your graphing calculator, graph each of the following: 3. 4.

Standard Form Standard Form of a Line The standard form of a linear equation is , where and are not both zero. Generally taken to be integers Standard Form To graph an equation in standard form: 1. Write equation in standard form. 2. Let x = 0 and solve for y. This is your yintercept.

3. Let y = 0 and solve for x. This is your xintercept. 4. Connect the dots. Standard Form To graph an equation in standard form: 1. Let 2. Let Solve for

Solve for This is the intercept This is the intercept 3. line Draw Exercise 9a Without your graphing calculator, graph each of the following:

1. 2. Exercise 9b Without your graphing calculator, graph each of the following: 3. 4.

Exercise 10 For an equation in standard form, Ax + By = C, what is the slope of the line in terms of A and B? Horizontal and Vertical Lines Horizontal Line The graph of is a horizontal line through .

6 B: (0.00, 5.00) 4 2 Vertical Line The graph of is a vertical line through . A: (4.00, 0.00)

5 -2 Exercise 11 Graph each of the following: 1. 2. Find Slope & Rate of Change Graph Equations of Lines

1. 2. 3. 4. Objectives: To find the slope of a line given 2 points To classify a line based on its slope

To find the slope of parallel and perpendicular lines To graph the equation of a line using slope-intercept and standard form of a line