Geometry Section 3.5.

Slides:

Advertisements

Similar presentations

Parallel & Perpendicular Slopes II

Advertisements

Writing Equations of a Line

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

EXAMPLE 1 Write an equation of a line from a graph

Warm up Write an equation given the following info:

Y – Intercept of a Line The y – intercept of a line is the point where the line intersects or “cuts through” the y – axis.

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.

2.4 Write Equations of Lines

Write an equation given the slope and a point

Parallel and Perpendicular Lines

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

3.5 Write and Graph Equations of Lines

EXAMPLE 1 Write an equation of a line from a graph

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

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?

Warm up Recall the slope formula:

3.5 Write and Graph Equations of Lines You will find equations of lines. Essential Question: How do you write an equation of a line?

Geometry: Chapter and 3.7: Writing equations for Parallel and Perpendicular Lines.

1. If 2x + 5y = –20 and x = 0, what is y? ANSWER –4

4-9 Slopes of Parallel and Perpendicular Lines Warm Up

1. If 2x + 5y = –20 and x = 0, what is y? ANSWER –4

1. If 2x + 5y = –20 and x = 0, what is y? ANSWER –4

Writing Equations of a Line

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

Writing Linear Equations in Slope-Intercept Form

Quick Graphs of Linear Equations

Writing Equations of a Line

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

Y – Intercept of a Line The y – intercept of a line is the point where the line intersects or “cuts through” the y – axis.

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

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

Writing Equations of Lines

Writing Linear Equations Given Two Points

3.5 Write and Graph Equations of Lines

SLOPE OF A LINE.

Objectives Identify and graph parallel and perpendicular lines.

5-6 Parallel and Perpendicular Lines

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

Writing the Equation of a Line

Determining an Equation of a Line

Writing Linear Equations Given Two Points

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

EXAMPLE 1 Write an equation of a line from a graph

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

Warm up Write an equation given the following information.

Graphing Systems of Equations

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:

Writing Equations of a Line

Warm up Write an equation given the following info:

Objective graph linear equations using slope-intercept form.

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

Solve Systems of Equations by Graphing

5.4 Finding Linear Equations

PERPENDICULAR LINES.

Parallel and Perpendicular Lines

Objectives: To graph lines using the slope-intercept equation

Warm Up x – 5 = 0 Write the Standard Form equation of

Warm-Up 1.) Using the point slope formula find the equation of a line with slope -2 , passing through the point (1, 3) 2.) Graph the line y = 3x + 4.

Chapter 4 Review.

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:

3.5 Write and Graph Equations of Lines

Slope-Intercept Form.

Presentation transcript:

Geometry Section 3.5

EXAMPLE 1 Write an equation of a line from a graph Write an equation of the line in slope- intercept form. SOLUTION STEP 1 Find the slope. Choose two points on the graph of the line, (0, 4) and (3, –2). m 4 – (– 2) 0 – 3 = 6 – 3 = = – 2 STEP 2 Find the y-intercept. The line intersects the y-axis at the point (0, 4), so the y-intercept is 4.

Write an equation of a line from a graph EXAMPLE 1 Write an equation of a line from a graph STEP 3 Write the equation. mx + b y = Use slope-intercept form. y = –2x + 4 Substitute – 2 for m and 4 for b.

EXAMPLE 2 Write an equation of a parallel line Write an equation of the line passing through the point (– 1, 1) that is parallel to the line with the equation y = 2x – 3. SOLUTION STEP 1 Find the slope m. The slope of a line parallel to y = 2x –3 is the same as the given line, so the slope is 2. STEP 2 Find the y-intercept b by using m = 2 and (x, y) = (– 1, 1).

Write an equation of a parallel line EXAMPLE 2 Write an equation of a parallel line y mx + b = Use slope-intercept form. 1 = 2 (–1 ) + b Substitute for x, y, and m. 3 = b Solve for b. Because m = 2 and b = 3, an equation of the line is y = 2x + 3.

Write an equation of a perpendicular line EXAMPLE 3 Write an equation of a perpendicular line Write an equation of the line j passing through the point (2, 3) that is perpendicular to the line k with the equation y = – 2x + 2. SOLUTION STEP 1 Find the slope m of line j. Line k has a slope of – 2. – 2 m = – 1 The product of the slopes of lines is – 1. 1 2 m = Divide each side by – 2.

Write an equation of a perpendicular line EXAMPLE 3 Write an equation of a perpendicular line 1 2 STEP 2 Find the y-intercept b by using m = and (x, y) = (2, 3). mx + b y = Use slope-intercept form. 3 = 1 2 ( 2 ) + b Substitute for x, y, and m. 2 = b Solve for b.

EXAMPLE 3 Write an equation of a perpendicular line Because m = and b = 2, an equation 1 2 of line j is y = x + 2. You can check that the lines j and k are perpendicular by graphing, then using a protractor to measure one of the angles formed by the lines.

EXAMPLE 5 Graph a line with equation in standard form Graph 3x + 4y = 12. SOLUTION The equation is in standard form, so you can use the intercepts. STEP 1 Find the intercepts. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. 3x +4y = 12 3x +4y = 12 3x +4 ( 0 ) = 12 3 ( 0 ) + 4y = 12 x = 4 y = 3

EXAMPLE 5 Graph a line with equation in standard form STEP 2 Graph the line. The intercepts are (4, 0) and (0, 3). Graph these points, then draw a line through the points.