Previously you learned one strategy for writing a linear equation when given the slope and a point on the line. In this lesson you will learn a different.

Slides:



Advertisements
Similar presentations
Warm Up Find the slope of the line containing each pair of points.
Advertisements

Writing Equations of a Line
Write an equation given the slope and a point
Write an equation given the slope and a point EXAMPLE 2 Write an equation of the line that passes through (5, 4) and has a slope of –3. Because you know.
Writing and Graphing Equations of Lines
Objectives Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Recall from Lesson 2-3 that.
The point-slope form of a linear equation of a non- vertical line is given by: Point-Slope Form of a Linear Equation.
3.4 Graph of Linear Equations. Objective 1 Use the slope-intercept form of the equation of a line. Slide
Solve an “and” compound inequality
10.2 Point-Slope and Standard forms of Linear Equations CORD Math Mrs. Spitz Fall 2006.
Chapter Point slope Form.
EXAMPLE 4 Write an equation given two points
Writing Linear Functions
1 The graph of y = 2x + 3 is shown. You can see that the line’s y -intercept is 3, and the line’s slope m is 2 : m =2 = rise run = 2121 Slope-Intercept.
Section 8-3 Chapter 1 Equations of Lines and Linear Models
2.4 Writing Equations for Linear Lines
Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.
1.Given slope (m) and y-intercept (b) create the equation in slope- intercept form. 2. Look at a graph and write an equation of a line in slope- intercept.
Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.
2.4 Essential Questions What is the point-slope form?
2.4 W RITING L INEAR F UNCTIONS Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Objectives.
ALGEBRA 1 Lesson 5-4 Warm-Up. ALGEBRA 1 “Point-Slope Form and Writing Linear Equations” (5-4) (5-3) What is “point- slope form”? How can you use point-slope.
Solve each equation for y. 1. 3x + y = 52. y – 2x = x – y = x + 4y = 85. 9y + 3x = 16. 5y – 2x = 4 Clear each equation of decimals x.
Point-Slope Form 4-7 Warm Up Lesson Presentation Lesson Quiz
EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.
GEOMETRY HELP Find and compare the slopes of the lines. Each line has slope –1. The y-intercepts are 3 and –7. The lines have the same slope and different.
5-6 Point-Slope Form Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.
Writing an Equation of a Line I can…. determine the equation of a line and/or graph a linear equation Unit 1 Basics of Geometry.
Chapter 3 Section 4. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Writing and Graphing Equations of Lines Use the slope-intercept.
Point-Slope Form 4-7 Warm Up Lesson Presentation Lesson Quiz
Point-Slope Form 4-7 Warm Up Lesson Presentation Lesson Quiz
CONFIDENTIAL 1 Algebra1 Point-Slope Form. CONFIDENTIAL 2 Warm Up Write the equation that describes each line in slope-intercept form. 1) slope = 3, y-intercept.
Use point-slope form to write an equation EXAMPLE 3 Write an equation in point-slope form of the line shown.
Systems of Equations: Substitution
Use the substitution method
Holt Algebra Writing Linear Functions Recall from Lesson 2-3 that the slope-intercept form of a linear equation is y= mx + b, where m is the slope.
Finding Linear Equations Section 1.5. Lehmann, Intermediate Algebra, 4ed Section 1.5Slide 2 Using Slope and a Point to Find an Equation of a Line Find.
Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.
Parallel and Perpendicular Lines Honors Math – Grade 8.
5.3 Write Linear Equations in Point-Slope Form Big Idea: -Verify that a point lies on a line, given an equation of a line. -Derive linear equations by.
To write another equivalent equation, multiply each side by x – 12y = 8 To write one equivalent equation, multiply each side by 2. SOLUTION Write.
Solve an “and” compound inequality
Lesson 1.  Example 1. Use either elimination or the substitution method to solve each system of equations.  3x -2y = 7 & 2x +5y = 9  A. Using substitution.
Holt Algebra Point-Slope Form Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. (–2, 8) and (4, 2) 3. (3,
Point-Slope Form Linear Equations in Two Variables.
Holt McDougal Algebra Point-Slope Form Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.
5-4 Point-Slope Form and Writing Linear Equations Hubarth Algebra.
Writing Equations of a Line
Point-Slope Form and Writing Linear Equations
Writing Linear Equations in Slope-Intercept Form
Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.
Using the Point-Slope Form
Learning Targets Graph a line and write a linear equation using point-slope form. Write a linear equation given two points. Warm Up Find the slope of the.
Writing Equations of a Line
Chapter 3 Section 4.
Solving Systems using Substitution
Warm Up Find the slope of the line containing each pair of points.
Point-Slope Form and Writing Linear Equations
Writing Linear Functions
Solving Multi-Step Equations
Objective Find slope by using the slope formula..
Writing Linear Equations Given Two Points
Example 1A: Graphing by Using Slope and y-intercept
12 Systems of Linear Equations and Inequalities.
Point-Slope Form 5-7 Warm Up Lesson Presentation Lesson Quiz
Writing Equations of a Line
Example 2B: Solving Linear Systems by Elimination
Module 11-3 Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.
WARM UP 3 WRITING EQUATIONS Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. (Lesson.
Presentation transcript:

Previously you learned one strategy for writing a linear equation when given the slope and a point on the line. In this lesson you will learn a different strategy – one that uses the point-slope form of an equation of a line. Using the Point-Slope Form POINT-SLOPE FORM OF THE EQUATION OF A LINE The point-slope form of the equation of the nonvertical line that passes through a given point (x 1, y 1 ) with a slope of m is y – y 1 = m (x – x 1 ).

Multiply each side by (x – 2). Write an equation of the line. Use the points (2, 5) and (x, y). Use formula for slope. SOLUTION You are given one point on the line. Let (x, y) be any point on the line. m =m = y – 5 x – 2 The graph shows that the slope is. Substitute for m in the formula for slope y – 5 x – 2 = 2323 Substitute for m y – 5 = 2323 (x – 2) 2323 The equation y – 5 = (x – 2) is written in point-slope form. Developing the Point-Slope Form Because (2, 5) and (x, y) are two points on the line, you can write the following expression for the slope of the line.

Using the Point-Slope Form You can use the point-slope form when you are given the slope and a point on the line. In the point-slope form, (x 1, y 1 ) is the given point and (x, y) is any other point on the line. You can also use the point-slope form when you are given two points on the line. First find the slope. Then use either given point as (x 1, y 1 ).

Using the Point-Slope Form SOLUTION First find the slope. Use the points (x 1, y 1 ) = (–3, 6) and (x 2, y 2 ) = (1, –2). m =m = y 2 – y 1 x 2 – x 1 –2 – 6 1 – (–3) = –8 4 = = –2 Write an equation of the line shown below.

Add 6 to each side. Write point-slope form. Substitute for m, x 1 and y 1. Simplify. Use distributive property. Then use the slope to write the point-slope form. Choose either point as (x 1, y 1 ). y – y 1 = m (x – x 1)y – y 1 = m (x – x 1) y – 6 = –2[x – (–3)] y – 6 = –2(x + 3) y – 6 = –2 x – 6 y = –2 x Using the Point-Slope Form SOLUTION Write an equation of the line shown below.

Use the information to write a linear model for optimal running pace, then use the model to find the optimal running pace for a temperature of 80° F. MARATHON The information below was taken from an article that appeared in a newspaper. Modeling a Real-Life Situation

Writing and Using a Linear Model SOLUTION Let T represent the temperature in degrees Fahrenheit. From the article, you know that the optimal running pace at 60° F is 17.6 feet per second so one point on the line is (T 1, P 1 ) = (60, 17.6). Find the slope of the line.  m = – 0.35– 0.35 change in P change in T == – 0.06 Use the point-slope form to write the model. P – P 1 = m (T – T 1 ) Write the point-slope form. P – 17.6 = (– 0.06)(T – 60) Substitute for m, T 1, and P 1. P – 17.6 = – 0.06T Use distributive property. P = –0.06T Add 17.6 to each side. Let P represent the optimal pace in feet per second.

Use the model P = –0.06T to find the optimal pace at 80° F. P = – 0.06(80) = 16.4 C HECK A graph can help you check this result. You can see that as the temperature increases the optimal running pace decreases. At 80° F the optimal running pace is 16.4 feet per second. Writing and Using a Linear Model SOLUTION