EXAMPLE 2 Identify parallel lines

Slides:

Advertisements

Similar presentations

Parallel & Perpendicular Slopes II

Advertisements

Writing Equations of a Line

EXAMPLE 1 Write an equation of a line from a graph

2.4 Write Equations of Lines

Write an equation given the slope and a point

Parallel and Perpendicular Lines

Parallel & Perpendicular Lines Parallel Lines m = 2/1 What is the slope of the 2 nd line?

1. (1, 4), (6, –1) ANSWER Y = -x (-1, -2), (2, 7) ANSWER

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.

SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.

For example: Could you tell that the equations y=2x +1 and y= 2x-7 have no solution? Can you look at a system of linear equations and tell how many solutions.

 Graph the following two lines:  1.  2.  Write an equation of the line that passes through (-3,3) and is parallel to the line y=-2x+1.

EXAMPLE 3 Write an equation of a line given two points

EXAMPLE 1 Write an equation of a line from a graph

Write an equation given two points

EXAMPLE 1 Find slopes of lines in a coordinate plane Find the slope of line a and line d. SOLUTION Slope of line a : m = – 1 Slope of line d : m = 4 –

Section 1.1 Slopes and Equations of Lines

EXAMPLE 4 Use coordinate geometry SOLUTION One way is to show that a pair of sides are congruent and parallel. Then apply Theorem 8.9. First use the Distance.

5.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Equations of Parallel and Perpendicular Lines.

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

Slopes of Parallel and Perpendicular Lines (3.6) Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and.

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

2.4 Essential Questions What is the point-slope form?

EXAMPLE 5 Graph real-world functions CABLE A cable company charges new customers $40 for installation and $60 per month for its service. The cost to the.

1.6 Warm Up 1.Find the slope between the points: 1.(9,3) & (-1, -6) _______________ 2.(4, -3) & (0, -3) _______________ 3.(2, 1) & (-5, 8) ________________.

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.

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

EXAMPLE 1 Identifying Slopes and y -intercepts Find the slope and y -intercept of the graph of the equation. a. y = x – 3 b. – 4x + 2y = 16 SOLUTION a.

Notes Over 5.2 Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form.

Notes Over 2.1 Graphing a Linear Equation Graph the equation.

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.

Example 2 Positive and Negative Slope Find the slope of the line. a. = run rise m = x1x1 x2x2 y1y1 y2y2 – – – – = 4 5 =

EXAMPLE 4 Write an equation of a line from a graph Gym Membership The graph models the total cost of joining a gym. Write an equation of the line. Explain.

. 5.1 write linear equation in slope intercept form..5.2 use linear equations in slope –intercept form..5.3 write linear equation in point slope form..5.4.

Example 2 Graphing Using Slope-Intercept Form 1

Geo A Chapter 7 Writing Linear Equations Write the point-slope form of the line that passes through the point (-3, -1) and has a slope of 1.

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 )

Use point-slope form to write an equation EXAMPLE 3 Write an equation in point-slope form of the line shown.

Find slope in real life EXAMPLE 1 Skateboarding A skateboard ramp has a rise of 15 inches and a run of 54 inches. What is its slope ? SOLUTION slope =

Warm-Up Exercises ANSWER $6 3. You play tennis at two clubs. The total cost C (in dollars) to play for time t (in hours) and rent equipment is given by.

EXAMPLE 2 Determine whether lines are parallel or perpendicular Determine which lines, if any, are parallel or perpendicular. Line a: y = 5x – 3 Line b:

Classify parallel and perpendicular lines EXAMPLE 4 Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (– 2, 2) and (0, –

Slope Formula. m = y₂ - y₁ x₂ - x₁ (x₁, y₁ ) and (x₂, y₂ ) Ordered pairs.

Objective - To write equations given the slope and a point using Point-Slope Form. Point-Slope Form Write the equation of a line in point-slope form that.

Writing Equations of a Line

Slope Intercept form. Geometry Unit 2-3, 2-4 Equations of lines Parallel and perpendicular slopes.

Parallel and Perpendicular Lines

ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.

Find the equation of the tangent line for y = x2 + 6 at x = 3

EXAMPLE 4 Use coordinate geometry

Writing Equations of a Line

Parallel and Perpendicular Lines

3-3: Slopes of Lines.

Lines in the Plane Property of Texas Tech University

Writing Equations of Lines

Writing Linear Equations Given Two Points

3.5 Write and Graph Equations of Lines

Mrs. Allouch JEOPARDY Unit 8.

EXAMPLE 1 Find slopes of lines in a coordinate plane

The Point-Slope Form of the Equation of a Line

Write the equation of the line.

y – y1 = m (x – x1) Topic: Writing Equations in Point-Slope Form

EXAMPLE 1 Write an equation of a line from a graph

EXAMPLE 1 Find slopes of lines in a coordinate plane

Writing Equations of a Line

WARM UP Find the equation of the line that passes through (3, 4), (6,8)? Find the slope of the line that passes through (-4,-8), (12,16)? Find the equation.

Chapter 4 Review.

Presentation transcript:

EXAMPLE 2 Identify parallel lines Find the slope of each line. Which lines are parallel? SOLUTION Find the slope of k1 through (– 2, 4) and (– 3, 0). m1 = 0 – 4 – 3 – (– 2 ) = – 4 – 1 = 4 Find the slope of k2 through (4, 5) and (1, 3). m2 1 – 5 3 – 4 = = – 4 – 1 = 4

EXAMPLE 2 Identify parallel lines Find the slope of k3 through (6, 3) and (5, – 2). m3 – 2 – 3 5 – 6 = = – 5 – 1 5 Compare the slopes. Because k1 and k2 have the same slope, they are parallel. The slope of k3 is different, so k3 is not parallel to the other lines.

GUIDED PRACTICE for Example 2 Line m passes through (–1, 3) and (4, 1). Line t passes through (–2, –1) and (3, – 3). Are the two lines parallel? Explain how you know. SOLUTION Find the slope of m through (– 1, 3) and (4, 1). m1 = 3 – 1 – 1 – 4 = 2 – 5 = 2 5 –

GUIDED PRACTICE for Example 2 Find the slope of t passes through (– 2, – 1) and (1, – 3). m2 – 1 – (– 3 ) –2 – 3 = = 2 – 5 = 2 5 – Compare the slopes. Because m and t have the same slope, they are parallel.