When we are given two points, we can use the slope formula to find the slope of the line between them. Example: You are given the points (4, 7) and (2,

Slides:

Advertisements

Similar presentations

Parallel & Perpendicular Slopes II

Advertisements

1.4 Linear Equations in Two Variables

3.7 Equations of Lines in the Coordinate Plane

Writing an Equation of a Line

Writing Linear Equations Using Slope Intercept Form

Parallel Lines. We have seen that parallel lines have the same slope.

Writing Equations Index Card Activity.

Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

2.2 Linear Equations.

The equation of a line - Equation of a line - Slope - Y intercept

2.4 Write Equations of Lines

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

SOLUTION EXAMPLE 3 Determine whether lines are perpendicular Line a: 12y = –7x + 42 Line b: 11y = 16x – 52 Find the slopes of the lines. Write the equations.

Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes.

 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.

Drill #18 Find the x- and y– intercepts of the following equations in standard form, then graph each equation: 1. 2x – 2y = x + 4y = x.

Drill #19 Determine the value of r so that a line through the points has the given slope: 1. ( 2 , r ) , ( -1 , 2 ) m = -½ Find the slope of the following.

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.

3-7 Equations of Lines in the Coordinate Plane

Notes Over 5.3 Write an equation in slope-intercept form of the line that passes through the points.

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

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.

Parallel lines Lines that are parallel have the same slope or gradient x y m1m1 m2m2  m 1 = m 2.

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:

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)

Linear Equations Objectives: -Find slope of a line - Write 3 different forms of linear equations Mr. Kohls.

Drill #23 Determine the value of r so that a line through the points has the given slope: 1. ( r , -1 ) , ( 2 , r ) m = 2 Identify the three forms (Point.

SOLUTION EXAMPLE 3 Determine whether lines are perpendicular Line a: 12y = – 7x + 42 Line b: 11y = 16x – 52 Find the slopes of the lines. Write the equations.

5.3 Slope-intercept form Identify slope and y-intercept of the graph & graph an equation in slope- intercept form. day 2.

 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.

Aim: How do we find points of intersection? What is slope? Do Now: Is the function odd, even or neither? 1)y - x² = 7 2)y = 6x - x⁷ 3)y = √ x⁴ - x⁶ 4)Find.

3.6 Finding the Equation of a Line

How to Write an Equation of a Line Given TWO points

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

Parallel & Perpendicular Lines

Writing Equations of Lines

Writing Linear Equations in Slope-Intercept Form

OBJECTIVE I will use slope-intercept form to write an equation of a line.

3.3: Point-Slope Form.

Chapter 1 Linear Equations and Linear Functions.

Equations of Lines in the Coordinate Plane

Chapter 1: Lesson 1.3 Slope-Intercept Form of a Line

Warm up (10/28/15) Write an equation given the following info:

PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane

SLOPE OF A LINE.

Warm up (3/28/17) Write an equation given the following info:

Chapter 1 Linear Equations and Linear Functions.

Writing the Equation of a Line

Linear Equations & Functions

The Point-Slope Form of the Equation of a Line

Writing Linear Equations Given Two Points

Example 1A: Graphing by Using Slope and y-intercept

2-4: Writing Linear Equations Using Slope Intercept Form

PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints P(5, 2) and Q(1, –4). Step 1 Graph PQ. The perpendicular.

Warm up Write an equation given the following information.

Warm up Write an equation given the following info:

Warm up Write an equation given the following info:

Warm up Write an equation given the following info:

Slope-intercept Form of Equations of Straight Lines

Warm up Write an equation given the following info:

Section 3.3 The Slope of a Line.

Substitute either point and the slope into the slope-intercept form.

Find the y-intercept and slope

5.4 Finding Linear Equations

Equations of Lines.

Parallel and Perpendicular Lines

PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane (coplanar) Equations: Same Slopes Different y-intercepts.

Warm up (10/22/14) Write an equation given the following info:

Presentation transcript:

When we are given two points, we can use the slope formula to find the slope of the line between them. Example: You are given the points (4, 7) and (2, 6). Find the slope. m = rise = y 2 – y 1 = 6 – 7 = 1 run x 2 – x 1 2 – 4 2

Step 1: Find the slope. Substitute the coordinates of the two given points into the formula for slope, m = y 2 – y 1 x 2 – x 1 Step 2: Find the y-intercept. Substitute the slope m and the coordinates of one of the points into the slope-intercept form, y = mx +b, and solve for the y-intercept. Step 3: Write an equation of the line. Substitute the slope m and the y-intercept b into the slope-intercept form, y = mx + b.

Write an of a line that passes through the points (3, 5) and (4, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 7 – 5 = 2 = 2 x 2 – x 1 4 – 3 1 Now we must find the y-intercept. y = mx + b 5 = 2(3) + b 5 = 6 + bSubtract 6 from both sides. -1 = b Now let’s write the equation of the line. y = mx + b y = 2x – 1

Write an equation of a line that passes through the points (9, 4) and (8, 7). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 7 – 4 = 3 = -3 x 2 – x 1 8 – 9 -1 Now we must find the y-intercept. y = mx + b 4 = -3(9) + b 4 = bAdd 27 to both sides. 31 = b Now let’s write the equation of the line. y = mx + b y = -3x + 31

Write an equation of a line that passes through the points (6, 1) and (2, 4). First we must find the slope of the line. We need to use the slope formula to do this. m = y 2 – y 1 = 4 – 1 = 3 x 2 – x 1 2 – 6 -4 Now we must find the y-intercept. y = mx + b 1 = (-3/4)(6) + b 1 = bAdd 4.5 to both sides. 5.5 = b Now let’s write the equation of the line. y = mx + b y = (-3/4)x + 5.5

Two different nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. For example: The negative reciprocal of 4 is: -1/4 The negative reciprocal of -3 is: 1/3 The negative reciprocal of -2/3 is: 3/2 The negative reciprocal of 7/2 is: -2/7

Using the figure to the left, show that two of the lines are perpendicular. The slope of AB: m = 7 – 1 = 6 = The slope of BC: m = = 8 = Notice that these two lines have slopes that are negative reciprocals of each other. This means that they are perpendicular. A (-4, 7) B (-8, 1) C (4, -7) D (8, -1)

Write an equation of a line that is perpendicular to y = 6x – 3 and passes through the point (4, 5). y = mx + b 5 = (-1/6)(4) + b 5 = -2/3 + b 17/3 = b y = (-1/6)x + 17/3 Write an equation of a line that is perpendicular to y = (1/2)x + 3 and passes through the point (1, 4). y = mx + b 4 = -2(1) + b 4 = -2 + b 6 = b y = -2x + 6