Algebra I Systems and Linear Equations and Inequalities Line Graphing 4.31 Given a line equation, graph the line on a Cartesian Plane Use “Choose x, find y” to graph line EO 1 EO2EO Use slope intercept formula to graph a line EO1EO2EO3EO Given a line on a Cartesian Plane, formulate the equation of the line Assess slope and y-intercept to formulate line equation EO1EO2EO Given two points, find the equation of a line EO1EO2EO3EO Given one point and a parallel line formulate an equation EO1EO2EO3EO Given one point and a perpendicular line formulate an equation EO1EO2EO3EO

Algebra I 1.0 Real Numbers and Expressions 2.0 Equations and Inequalities in One Variable 3.0 Equations and Inequalities in Two Variables and Functions 4.0 Systems and Linear Equations and Inequalities 5.0 Polynomials 6.0 Factoring 7.0 Rational Expressions and equations 8.0 Rational Expressions and Equations 9.0 Rational Exponents, Radicals, and Complex Numbers The year-long Algebra I course segmented into nine units. Our focus is within Unit 4.0.

4.0 Systems of Linear Equations and Inequalities 4.1 Describe how the Cartesian Plane represents two- dimensional space 4.11 Designate the x and y axes on a Cartesian Plane 4.12 Identify the four quadrants on the Cartesian Plane 4.2 Point Graphing 4.21 Find location of point given a coordinate pair 4.22 Name the coordinate pair for any given point on the Cartesian Plane 4.3 Line Graphing 4.31 Given a line equation, graph the line on a Cartesian Plane 4.32 Given a line on a Cartesian Plane, formulate the equation of the line Course Unit Three Major Components of Unit Our line-graphing standard for the focus of instruction

4.3 Line Graphing 4.31 Given a line equation, graph the line on a Cartesian Plane Use “Choose x, find y” to graph line Use slope intercept formula to graph a line 4.32 Given a line on a Cartesian Plane, formulate the equation of the line Assess slope and y- intercept to formulate line equation Given two points, find the equation of a line Given one point and a parallel line formulate an equation Given one point and a perpendicul ar line formulate an equation Terminal Objectives Our line- graphing standard for the focus of instruction

4.311 Use “Choose x, find y” to graph a line. Use substitution to solve for one variable. Graph ordered pairs on a Cartesian plane. Identify trends in number functions. Enabling Objective 1 Enabling Objective 2 Enabling Objective 3 y = -3x +8 (2, 2) (4, 4) xy (2, 2) (4, 4) Terminal Objective

4.321 Assess slope and y-intercept to formulate line equation. State whether a given line will have a positive or negative slope. State the y- intercept of a given line. Calculate slope based on two points along the line. Terminal Objective Enabling Objective 1 Enabling Objective 2 Enabling Objective 3 y = -2x + 5 “-2 (m) is the slope of this line equation. When m < 0 the slope is negative. Therefore, this line has a negative slope.” If y = mx + b, then y = 4/3x - 4

4.321 Use slope-intercept formula to graph a line. Define slope. Identify parts of equation y = mx + b. Be able to find y-intercept on a graph of a line. Relate sign of m to positive or negative slope. Terminal Objective Enabling Objective 1 Enabling Objective 2 Enabling Objective 3 Enabling Objective 4 y = mx + b m = -2 b = 5 y = -2x + 5 slope y-intercept Slope is the measure of steepness of a line Slope Let x = 0 m < 0 = negative slope m > 0 = positive slope

4.322 Given two points, find the equation of the line. Calculate the slope of the line that connects the given points. Substitute the coordinates of one point into equation, then solve to find the y-intercept. Identify the parts of a line equation that determine characteristics of the line. Explain why x and y variables are part of line equation. Terminal Objective Enabling Objective 1 Enabling Objective 2 Enabling Objective 3 Enabling Objective 4 Given: (2, 3) and (6, 4) So, y = 1/4 x + 5/2 Therefore, (x + 3) ¾ = (y + 2)(x + 3) (x + 3) 4(3x + 9) = (y + 2)4 4 y = ¾ x + ¼ y –intercept = ¼ y = ½ x + 5 and y = 2x - 5 “The slopes are not the same so the lines are not parallel. Both lines have unknown x and y values because the lines are infinite.”

4.323 Given one point and a parallel line, find the equation of a line. State how slopes of parallel lines are related. State that y- intercepts of parallel lines must not be the same. Explain what makes two lines dependent. Demonstrate that two parallel lines on a plane can never intersect. Terminal Objective Enabling Objective 1 Enabling Objective 2 Enabling Objective 3 Enabling Objective 4 y = 2x – 5 and y = 2x + 4 “ The slopes are the same so the lines are parallel. The y-intercepts are different otherwise the lines would be the same line.” I see that the slopes of the parallel lines is -1 My two points are (-2, 2) I can find the y-intercept as 2= (-1)(-2) +b = 0 Therefore y = -x + 0 “These lines are dependent because their points are on the same line.”

4.324 Given one point and a perpendicular line, find the equation of a line. Find the slope of a line when the slope of a perpendicular line has been given. Explain how slopes of perpendicular lines are related. Demonstrate that perpendicular lines intersect at one point. Define perpendicular. Terminal Objective Enabling Objective 4 Enabling Objective 3 Enabling Objective 2 Enabling Objective 1 “A line is perpendicul ar to another if they meet at 90 degrees.” 5x+4y-20=0 5x+4y=20 x intercept occurs when y=0 5x=20 x=4 4 is the x intercept. 4x+3y-12=0 3y=12-4x y=4-4x/3 -4/3 is the slope of the line. The slope of a line that is perpendicular is the negative reciprocal of the slope which in this case is 3/4 “The slope of a line that is perpendicular is the negative reciprocal of the slope.” 5x+4y-20=0 5x+4y=20 5x=20 x=4 4x+3y-12=0 3y=12-4x y=4-4x/3 -4/3 is the slope of the line.

4.311 Use “Choose x, find y” to graph line EO1EO2EO Use slope intercept formula to graph a line EO1EO2EO3EO Assess slope and y- intercept to formulate line equation EO1EO2EO Given two points, find the equation of a line EO1EO2EO3EO Given one point and a parallel line formulate an equation EO1EO2EO3EO Given one point and a perpendicular line formulate an equation EO1EO2EO3EO4 Content Delivery Formative Assessment/ Analysis Access Prior Knowledge Introduce New Information Vocabulary Formative Assessment/ Analysis Examples/ Demonstration Guided Practice Independent Practice Formative Assessment/ Analysis Remediation/Enrichment Summative Assessment