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3-5 LINES IN THE COORDINATE PLANE M11.B A OBJECTIVES: 1)TO GRAPH LINES GIVEN THEIR EQUATIONS 2) TO WRITE EQUATIONS OF LINES
Vocabulary The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. Example: Y = 2x + 3 Y = 2x – 1 Y = 2x – 4
Example: Graph Lines in Slope- Intercept Form y = -2x + 4 y = ½ x -3 y = ¾ x
Vocabulary Standard Form of a Linear Equation – is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero. Example: Find A, B and C. -3x + 2y = 12
Example: Graphing Lines Using Intercepts Use the x and y intercept to graph 4x – 6y =24 “Hide and Divide”
Example: Graphing Lines Using Intercepts Graph -2x + 4y = -8 Graph 5x – 6y = 30
Example: Transforming from Standard Form to Slope-Intercept Form Graph -6x + 3y = 12
Graph using Slope-Intercept Form -5x + y = -3 -6x – 3y = 12
Vocabulary Point – Slope form – used for a nonvertical line through point (x ₁, y₁) where m = slope. y – y₁ = m( x – x₁)
Example: Using Point – Slope Form Write an equation of the line through point (3, 6) and with a slope of -8.
Using Point-Slope Form Example: Write an equation of the line with slope -1 that contains point P(2, -4)
Slope Formula Given two points: (x 1, y 1 ) and (x 2, y 2 ) m = y 2 – y 1 x 2 – x 1 Example: Find the slope of (3, -2) and (-5, 6)
Example: Equation of a Line Given Two Points Write an equation of the line through points G( 4, -9 ) and H( -1, 1).
Equation of a Line Given Two Points Write an equation of the line that contains the points P(5, 0) and Q(7, -3).
Slopes of Special Lines What is the slope of a horizontal line and a vertical line?
Example: Equation of Horizontal & Vertical Lines Write equations for the horizontal line and the vertical line that contains P(3, 2).
Equations of Horizontal and Vertical Lines Write equations of the horizontal and vertical lines that contain the point P(5, -1)
3.7 Equations of Lines in the Coordinate Plane The slope m of a line is the ratio `of the vertical change (rise) to the horizontal change (run) between.
Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D: determine the slope given a graph.
2.4 Writing the Equation of a Line. Review of Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m represents the slope.
Warm Up Find the slope of the line that passes through each pair of points 1.(3, 6) and (–1, 4) 2. (1, 2) and (6, 1) Course Using Slopes and Intercepts.
Writing Linear Equations Using Slope Intercept Form.
EXAMPLE 1 Write an equation of a line from a graph SOLUTION m 4 – (– 2) 0 – 3 = 6 – 3 = = – 2 STEP 2 Find the y -intercept. The line intersects the y -axis.
Chapter 3: Parallel and Perpendicular Lines 3-6 Lines in the Coordinate Plane.
Do Now. 2.3 Linear Functions and Slope-Intercept Form Learning Target: I can Graph linear equations I can write equations of lines.
Bellringer. Chapter 6: Section 2 Slope-Intercept Form.
GOAL 1 SLOPE OF PERPENDICULAR LINES 3.7 Perpendicular Lines in the Coordinate Plane Slopes of Perpendicular Lines Two nonvertical lines are perpendicular.
2-3C Finding an Equation of a Line 2-3C Finding an Equation of a Line Objectives: To write an equation of a line using the slope-intercept equation.
1.4 Linear Equations in Two Variables. Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x 2.
Unit 6 Notes Day 1 EQ: How do I find the x- and y-intercepts of linear equations?
UNIT 1B LESSON 2 REVIEW OF LINEAR FUNCTIONS. Equations of Lines The horizontal line through the point (2, 3) has equation The vertical line through the.
Algebra II w/ trig. Slope(m) is the ratio change in a vertical direction to the corresponding change in the horizontal direction. m = Where (x 1.
Warm up Write the equation of the line passing through the given point with the given slope. Then graph the line. 1. (-4, -3), m = 2. (8, 2), m =
Y x Objective - To graph linear equations using the slope and y-intercept. x Complete the table and graph y-intercept b = -1 Slope-Intercept.
1.3Linear Equations in Two Variables Slope of a Line Find the slope of the lines passing through… a.(-2,0) and (3,1) b.(-1,2) and (2,2) c.(4,-3) and (4,5)
WRITING AN EQUATION OF A LINE DETERMINE THE EQUATION OF A LINE AND/OR GRAPH A LINEAR EQUATION.
Writing Equations of a Line. Various Forms of an Equation of a Line. Gradient-Intercept Form Standard Form Point-Gradient Form.
WARM UP 1. Explain how to graph a linear equation written in slope-intercept form. 2. Explain how to graph a linear equation written in point-slope form.
Bellringer. Chapter 6: Section 5 Parallel and Perpendicular Lines.
Holt Geometry 3-6 Lines in the Coordinate Plane Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m =
First let’s review 5.1 Write the equation in slope-intercept form, given m = 3 ang b = (0,-2) Example m = 3, b = (0,-2) y = __ x + ___ y = mx + b.
2.3 Quick Graphs of Linear Equations p. 82. y x S LOPE- I NTERCEPT F ORM m is the slope b is the y -intercept The slope intercept form of a linear equation.
Graphing Linear Inequalities in Two Variables Objective: Graph all of the solutions to a linear inequality NCSCOS: 1.02, 3.03, 4.01.
Do Now Find the value of m undefined0.
Graphing Linear Equations By: Christine Berg Edited By: VTHamilton.
Holt Geometry 3-6 Lines in the Coordinate Plane 3-6 Lines in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.
The Linear Function. The word LINEAR means having to do with a straight line. Linear relationships are also called linear functions. What we have learned:
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