Slope Lesson 2-3 Algebra 2.

Slides:



Advertisements
Similar presentations
1.4 Linear Equations in Two Variables
Advertisements

Slope of a Line 11-2 Warm Up Problem of the Day Lesson Presentation
Linear Functions.
Perpendicular Lines and Slope
~ Chapter 6 ~ Algebra I Algebra I Solving Equations
Slope and Rate of Change Equations of Lines
Determining if Lines are Parallel or Perpendicular Parallel linesPerpendicular lines Slopes are the same Slopes are opposite reciprocals (assume no vertical.
Section 7.3 Slope of a Line.
Chapter 4: Matrices Lesson 9: Perpendicular Lines Mrs. Parziale.
Objective The student will be able to:
2.5 Linear Equations. Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5)
EXAMPLE 2 Find a negative slope Find the slope of the line shown. m = y 2 – y 1 x 2 – x 1 Let (x 1, y 1 ) = (3, 5) and (x 2, y 2 ) = (6, –1). –1 – 5 6.
Warm Up for 9.6 Find the distance and midpointbetween the following sets of points. (5, 19) and (-3, -1) (7, -16) and (-2, -1) (1, -4) and (0, 0) (-6,
I was clear on everything from the past lessons, except…
Chapter 8 Graphing Linear Equations. §8.1 – Linear Equations in 2 Variables What is an linear equation? What is a solution? 3x = 9 What is an linear equation.
EXAMPLE 1 Graph an equation of a circle Graph y 2 = – x Identify the radius of the circle. SOLUTION STEP 1 Rewrite the equation y 2 = – x
Slopes of Lines Chapter 3-3.
Chapter 4 Basic Algebra.
1.3 Linear Equations in Two Variables Objectives: Write a linear equation in two variables given sufficient information. Write an equation for a line.
4-1A Rate of Change and the Slope of a Line Using a Graph
Linear Equations in Two Variables MATH Precalculus S. Rook.
Slope of a Line Section 1.3. Lehmann, Intermediate Algebra, 3ed Section 1.3Slide 2 Introduction Two ladders leaning against a building. Which is steeper?
Evaluate each equation for x = –1, 0, and y = 3x 2. y = x – 7 3. y = 2x y = 6x – 2 –3, 0, 3 –8, –7, –6 3, 5, 7 –8, –2, 4 Pre-Class Warm Up.
Slope describes the steepness of a line By Angela Gallacher.
4.4 Slope of a Line Slope basically describes the steepness of a line.
Slopes and Parallel Lines Goals: To find slopes of lines To identify parallel lines To write equations of parallel lines.
Everything You Will Ever Need To Know About Linear Equations*
Slopes of lines Graphing Equation of Slope and Steepness Rate Parallel and Perpendicular.
3.4 – FIND AND USE SLOPES. Slope: measures the steepness of a line or the rate of change. Slope = m = Rise Run Up or down Left or right =
1 Warm UP Graph each equation and tell whether it is linear. (create the table & graph) 1. y = 3x – 1 2. y = x 3. y = x 2 – 3 yes Insert Lesson.
Linear Functions Slope and y = mx + b. Remember Slope… Slope is represented by m m = 0 Horizontal Line Vertical Line Slope up to the right Slope up to.
Slope of a Line Lesson 6.2.
The Slope of a Line. Finding Slope of a Line The method for finding the steepness of stairs suggests a way to find the steepness of a line. A line drawn.
Slope of a Line Slope basically describes the steepness of a line.
The Slope of a Line In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.
4.4 Slope of a Line. Slope – a measure of how steep a line is. Slope is the ratio of the vertical change to the horizontal change of a non- vertical line.
Lesson 2-3 Objective The student will be able to: 1) write equations using slope-intercept form. 2) identify slope and y-intercept from an equation.
8.2 Lines and Their Slope Part 2: Slope. Slope The measure of the “steepness” of a line is called the slope of the line. – Slope is internationally referred.
Algebra 1 Notes Lesson 5-6: Parallel and Perpendicular Lines.
Do Now Write the slope-intercept equation of this line.
WARM-UP Solve each equation for y 1) 2) Determine if the following points are on the line of the equation. Justify your answer. 3) (3, -1) 4) (0, 1)
Section 6.5: Parallel and Perpendicular Lines Objectives: Determine whether lines are parallel Determine whether lines are perpendicular Write equations.
Week 4 Functions and Graphs. Objectives At the end of this session, you will be able to: Define and compute slope of a line. Write the point-slope equation.
Pre-Algebra 11-2 Slope of a Line 11-2 Slope of a Line Pre-Algebra Homework & Learning Goal Homework & Learning Goal Lesson Presentation Lesson Presentation.
Slope of a Line. Slopes are commonly associated with mountains.
Slope of a Line 11-2 Warm Up Problem of the Day Lesson Presentation
Linear Functions.
Linear Functions.
Geometry Review on Algebra 1
Objective The student will be able to:
Linear Functions.
Objective The student will be able to:
Linear Functions.
2.5 Linear Equations.
Objectives Identify and graph parallel and perpendicular lines.
Warm-up: Check the equation y = 3x – x3 for symmetry.
Graphing Lines.
Linear Functions.
3-5: Vocabulary rise, run, slope point-slope form of a line
3-5: Vocabulary rise, run, slope point-slope form of a line
Linear Functions.
Linear Functions.
Linear Functions.
Section 3.6 Find and Use Slopes of Lines
Objective The student will be able to:
Linear Functions.
Objective The student will be able to:
Objective The student will be able to:
Click the mouse button or press the Space Bar to display the answers.
Linear Functions and Slope-Intercept Form Lesson 2-3
Presentation transcript:

Slope Lesson 2-3 Algebra 2

Slope Slope basically describes the steepness of a line If a line goes up from left to right, then the slope has to be positive Conversely, if a line goes down from left to right, then the slope has to be negative Beginning course details and/or books/materials needed for a class/project.

Slope Formula In order to use that formula we need to know, or be able to find 2 points on the line A schedule design for optional periods of time/objectives.

Procedure for Finding Slope (-3, 7) and (4, -6) To find the slope given two points: Determine the values of x1, x2, y1, and y2 Substitute the value of each variable in the formula and solve Simplify the fraction as much as possible DO NOT write the fraction as a mixed number of a decimal A list of procedures and steps, or a lecture slide with media.

Examples of Finding Slope (4, -1.5) & (3, 2.5) (1/2, 2/3) & (5/6, 1/4)

Horizontal & Vertical Lines Horizontal lines have a slope of zero (when 0 is on top of a fraction) Vertical lines have no slope (when 0 is under the fraction bar) m = 0 m = no slope

Your Turn: Find the slope of the line passing through each pair of points. Then Graph the line. (-1, 4) and (1, -2) (-2, -3) and (0, -5) (5, -4) and (5, 6) (2, -7) and (-3, -7) Objectives for instruction and expected results and/or skills developed from learning.

Graphing a Line Given a Point and Slope (-4, -3) and m = 2/3 To graph a line given a point on the line and the slope of the line: Plot the given point on graph paper From that point, use your slope to find another point on the line Connect your points to draw the line Example graph/chart.

More Graphing… (2, -1) and m = 3 (-3, -4) and m = -3/2

More Graphing… (-2, -1) and m = no slope (1, 4) and m = 0

Graph the line passing through the point (-3, -1) with m = -3 Your Turn… Graph the line passing through the point (-3, -1) with m = -3

Standard Form and Slope If a line is in the form Ax + By = C, we can use the following formula to find the slope: Relative vocabulary list.

Examples of Finding Slope Given Standard Form 5x – 4y = 8 15x + 3y = 17 Example graph/chart.

Parallel Lines & Slope Parallel lines have the same slope. Graph the line through (-1, 3) that is parallel to the line with equation x + 4y = -4. Find the slope of the line with the given equation Plot the point you are given Use the slope you found to graph another point Draw a line through the points

Your Turn… Graph the line through (2, -1) that is parallel to the line with equation 2x + 3y = 6. Conclusion to course, lecture, et al.

Perpendicular Lines & Slope The slopes of perpendicular lines are opposite reciprocals. What is a opposite reciprocal?

Perpendicular Lines & Slope Graph the line through (4, -2) that is perpendicular to the line with equation 3x – 2y = 6. Find the slope of the line with the given equation Find the opposite reciprocal of this slope Plot the point you are given Use the opposite reciprocal slope you found to graph another point Draw a line through the points

Your Turn… Graph the line through (-1, 5) that is perpendicular to the line with equation 5x – 3y = 3.

Answer this question in your warm-up book. How does slope apply to the steepness of roads? Include the following in your answer: A few sentences explaining the relationship between the grade of a road (the amount a road rises divided by the horizontal distance of the road) and the slope of a line A graph of y = 0.1x which corresponds to a 10% grade (The scale on your x- and y-axes should be the same.)