Find Slope & Rate of Change Graph Equations of Lines Objectives: 1.To find the slope of a line given 2 points 2.To classify a line based on its slope 3.To find the slope of parallel and perpendicular lines 4.To graph the equation of a line using slope-intercept and standard form of a line

Vocabulary SlopeRate of Change ParallelPerpendicular Parent FunctionIntercepts Slope-Intercept FormStandard Form

Objective 1 You will be able to find the slope between two points

Slope Anything that isn’t completely vertical has a slope. This is a value used to describe its incline or decline.

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

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 slope The slope m of a nonvertical line is the ratio of vertical change (the ryse) to the horizontal change (the run). 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, 2 k ) 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)

Objective 3

Parallel and Perpendicular parallel lines Two lines are parallel lines iff they are coplanar and never intersect. perpendicular lines Two lines are perpendicular lines iff they intersect to form a right angle.

Parallel and Perpendicular parallel lines Two lines are parallel lines iff they have the same slope. perpendicular lines 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?

Objective 4

Parent Functions family of functions parent function 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 FunctionsLinear Parent Function

Parent Functions family of functions parent function 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 FunctionsQuadratic Parent Function

Parent Functions family of functions parent function 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 FunctionsParent Function A group of functions that share common characteristics Simplest member of the family

Parent Functions All other linear functions can be formed with transformations on the parent function.

Intercepts Click me!

Slope-Intercept Slope

Slope-Intercept To graph an equation in slope-intercept form: Draw line

Exercise 8a Without your graphing calculator, graph each of the following:

Exercise 8b Without your graphing calculator, graph each of the following:

Standard Form 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 y - intercept. 3.Let y = 0 and solve for x. This is your x - intercept. 4.Connect the dots.

Standard Form To graph an equation in standard form: Draw line

Exercise 9a Without your graphing calculator, graph each of the following:

Exercise 9b Without your graphing calculator, graph each of the following:

Exercise 10 For an equation in standard form, A x + B y = C, what is the slope of the line in terms of A and B?

Horizontal and Vertical Lines

Exercise 11 Graph each of the following:

Find Slope & Rate of Change Graph Equations of Lines Objectives: 1.To find the slope of a line given 2 points 2.To classify a line based on its slope 3.To find the slope of parallel and perpendicular lines 4.To graph the equation of a line using slope-intercept and standard form of a line