6.5 Find an Equation for a Line Given the Slope and a Point We can find the equation of a line from knowing only its SLOPE and a POINT on the line.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Write an equation of a line from a graph

Advertisements

Warm up Graph the equation of the line using slope & y-intercept

Parallel and Perpendicular Lines

Lesson 5.1 Write Equations in Slope-Intercept Form.

Slope Intercept Form.

4.7 Graphing Lines Using Slope Intercept Form

 An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept.  The y-intercept is where.

Find slope and y-intercept given an equation in standard form. 5.5 day 2 3x - 6y = 12.

Do Now Find the slope of the line passing through the given points. 1)( 3, – 2) and (4, 5) 2)(2, – 7) and (– 1, 4)

Graphing Linear Equations in Slope-Intercept Form.

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Objective- To use slope and y-intercept to

7.5 – Special Linear Systems

WRITING LINEAR EQUATIONS 5.1 AND 5.2. WRITING A LINEAR EQUATION GIVEN THE SLOPE AND Y-INTERCEPT Use the equation y = mx + b The slope is the m in the.

EXAMPLE 1 Write an equation of a line from a graph

Write an equation given two points

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Classifying Systems of Linear Equations

Writing the Equation of a Line

Slope Intercept Form. Y = mx + b m is the slope b is the y-intecept (0, b) Your equation must say “y = “ Example: Y = 3x + 8 m = 3 Y-intercept (0,8) Y.

Writing Equations of Lines. Do Now: Answer each of the following questions based on the graph 1.What is the slope of the line? 2.What is the y-intercept?

Goal: Write a linear equation..  1. Given the equation of the line 2x – 5y = 15, solve the equation for y and identify the slope of the line.  2. What.

8-3 & 8-4: Graphing Linear Functions Mr. Gallo. Graphing Linear Functions  Linear Function:  The graph of this function is a ____________ _______. 

Lesson 5.6 Point-Slope Form of the Equation of a Line.

Writing equations given a point and the slope of a line

5-3 Slope Intercept Form A y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis. *Use can use the slope and y-intercept.

2.4 Writing Equations for Linear Lines

Objective I will identify the number of solutions a linear system has using one of the three methods used for solving linear systems.

Writing & Identifying Equations of Parallel & Perpendicular Lines Day 94 Learning Target: Students can prove the slope criteria for parallel and perpendicular.

3.6 Finding the Equation of a Line

Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.

WRITE EQUATIONS OF PARALLEL AND PERPENDICULAR LINES November 20, 2008 Pages

2.4 Essential Questions What is the point-slope form?

 Complete the tables x5x – xx

X and Y Intercepts.

Find the equation of the line that has... A B C D E F

Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b (slope – intercept form)

2 – 4: Writing Expressions of Lines (Day 1 ) Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

Ch 4.7 Objective: To use the slope and y-intercept to graph lines.

Big Idea : -Solve systems of linear equations by graphs.

2.4 “Writing Linear Equations” ***When writing equations of lines, substitute values for: y = mx + b Given: 1.Slope and y-intercept m = -3 b = 5 Step:

Notes Over 2.1 Graphing a Linear Equation Graph the equation.

Slope-Intercept Form. y=mx + b m is the SLOPE m is the SLOPE b is the Y-INTERCEPT (where the line crosses the y-axis) b is the Y-INTERCEPT (where the.

Point Slope Form. Write the equation of the line with slope 3 and passing through the point (1, 5). y – y 1 = m(x – x 1 )

Do Now 1)Write the slope-intercept equation of this line.

Systems of Equations Solving by Graphing Systems of Equations One way to solve equations that involve two different variables is by graphing the lines.

Warm up Recall the slope formula:

Solving Linear Systems by Substitution

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 3 Introduction to Graphing.

Graphing Linear Inequalities in Two Variables Objective: Graph all of the solutions to a linear inequality.

By Carol Nicholson  When we have two lines on the same plane:

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 1.4, Slide 1 Chapter 1 Linear Equations and Linear Functions.

2-4 Writing Linear Equations Objectives Students will be able to: 1) write an equation of a line given the slope and a point on the line, or two points.

Solving Systems By Graphing. Warm – Up! 1. What are the 2 forms that equations can be in? 2. Graph the following two lines and give their x-intercept.

Systems of Equations. OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination.

Solving Systems By Graphing. Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept form for the equation of a line Slope = rise run.

Objective The student will be able to: solve systems of equations by graphing.

 An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept.  The y-intercept is where.

How to Write an Equation of a Line Given TWO points

Parallel and Perpendicular Lines

Chapter 1 Linear Equations and Linear Functions.

Writing Equations of a Line

Warm-up 3-7: Survey.

Solve a system of linear equation in two variables

Chapter 1 Linear Equations and Linear Functions.

Writing the Equation of a Line

EXAMPLE 1 Write an equation of a line from a graph

Geometry Section 3.5.

5.4 Finding Linear Equations

3.5 Write and Graph Equations of Lines

Presentation transcript:

6.5 Find an Equation for a Line Given the Slope and a Point We can find the equation of a line from knowing only its SLOPE and a POINT on the line.

Find the Equation of a Line Given its Slope and a Point Example #1 (1) Find the equation of a line with a slope of 2 that passes through (2,6) (2) Graph the line

Solution Substitute x = 2, y = 6, and m = 2 into the slope y-intercept form of the equation of a line, and solve for b. Substitute x = 2, y = 6, and m = 2 into the slope y-intercept form of the equation of a line, and solve for b. y = mx + b y = mx + b 6 = 2(2) + b 6 = 2(2) + b 6 = 4 + b 6 = 4 + b =b =b 2 = b 2 = b Therefore, the y-intercept is 2. Therefore, the y-intercept is 2. The equation of this line is y = 2x + 2 The equation of this line is y = 2x + 2

y = 2x + 2

Find the Equation of a Partial Variation Tamur knows that it costs $25 to take a taxi to school, which is 10 km from his home. He forgets what the fixed cost is, but remembers that the variable cost is $2/km. Tamur’s friend lives 12 km from his home. Tamur has $60 dollars to spend on the weekend. a) Find the fixed cost and write an equation that relates the cost, in dollars, of a trip to the distance in kilometers. a) Find the fixed cost and write an equation that relates the cost, in dollars, of a trip to the distance in kilometers. b) Find the cost of a 12 km trip. Can Tamur, who has $60 to spend, afford a round trip of this distance? b) Find the cost of a 12 km trip. Can Tamur, who has $60 to spend, afford a round trip of this distance?

Solution To find the fixed cost, substitute d = 10, C = 25, and m = 2 into the equation: To find the fixed cost, substitute d = 10, C = 25, and m = 2 into the equation: C = md + b C = md + b 25 = 2(10) + b 25 = 2(10) + b 25 = 20 + b 25 = 20 + b = b = b 5 = b 5 = b Therefore, the fixed cost for the taxi fare is $5. Therefore, the fixed cost for the taxi fare is $5. The equation is C = 2d + 5 The equation is C = 2d + 5

To find the cost of a 12-km trip, you can substitute d = 12 into the equation To find the cost of a 12-km trip, you can substitute d = 12 into the equation C = 2d + 5 C = 2d + 5 C = 2(12) + 5 C = 2(12) + 5 C = C = C = 29 C = 29 Therefore, the total cost of this fare will be $29. Since Tamur has $60, he does have enough money to go there and come back. Therefore, the total cost of this fare will be $29. Since Tamur has $60, he does have enough money to go there and come back.

Find the equation of a line that is parallel to x – y – 12 = 0 that passes through (2,-5)

Key Information: x – y – 12 = 0 Point on the line: (2, -5) First, rearrange into y= mx + b x – y – 12 = 0 y = x - 12 The slope of this line and a line parallel to it is 1. Substitute m = 1, x = 2, and y = -5 into the equation to solve for b. y = mx + b -5 = 1(2) + b -5 = 2 + b -7 = b Write the equation of the line in y = mx + b form y = x - 7