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3-5 Lines in the coordinate plane M11. B. 2. 2. 3. 11Lines 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 Formy = -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 InterceptsUse the x and y intercept to graph 4x – 6y =24 “Hide and Divide”
Example: Graphing Lines Using InterceptsGraph -2x + 4y = -8 Graph 5x – 6y = 30
Example: Transforming from Standard Form to Slope-Intercept FormGraph -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 (x₁ , y₁) where m = slope. y – y₁ = m( x – x₁)
Example: Using Point – Slope FormWrite an equation of the line through point (3, 6) and with a slope of -8.
Using Point-Slope FormExample: Write an equation of the line with slope -1 that contains point P(2, -4)
Slope Formula Given two points: (x1, y1) and (x2, y2) m = y2 – y1x2 – x1 Example: Find the slope of (3, -2) and (-5, 6)
Example: Equation of a Line Given Two PointsWrite an equation of the line through points G( 4, -9 ) and H( -1, 1).
Equation of a Line Given Two PointsWrite an equation of the line that contains the points P(5, 0) and Q(7, -3).
Slopes of Special LinesWhat is the slope of a horizontal line and a vertical line?
Example: Equation of Horizontal & Vertical LinesWrite equations for the horizontal line and the vertical line that contains P(3, 2).
Equations of Horizontal and Vertical LinesWrite equations of the horizontal and vertical lines that contain the point P(5, -1)
Objective - To graph linear equations using the slope and y-intercept.
Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D:
3.7 Equations of Lines in the Coordinate Plane
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.
Linear Equations Review. Find the slope and y intercept: y + x = -1.
Section 2.3 – Linear Functions and Slope-Intercept Form Consider a nonvertical line in the coordinate plane. If you move from any point on the line to.
3.5 Lines in the Coordinate Plane
Writing equations in slope intercept form
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.
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
Drill #19* Find the x- and y– intercepts of the following equations in standard form, then graph each equation: 1.2x – 2y = x + 4y = x + 3y.
Write an equation of a line by using the slope and a point on the line.
Algebra 1 Notes Lesson 5-6: Parallel and Perpendicular Lines.
Point Slope Form To write an equation with the slope and a point that is not the y intercept.
Warm-up: Find the measure of an interior and exterior angle of an 18-gon.
Slopes of Parallel and Perpendicular Lines. Different Forms of a Linear Equation Standard Form Slope-Intercept Form Point-Slope Form Standard.
3.5 Slope of a Line. What is Slope? Slope is a measure of the steepness of a line. When looking at a graph, we can determine slope by taking, or the vertical.
Distance On a coordinate plane Finding the length of a line segment.
1. Write the equation in standard form.
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