Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 282.3 LinesChapter 2 Section 3: LinesIn this section, we will…Find the slope of a line Identify the slope and the y-intercept of a line Graph lines given a point on the line and its slopeDetermine if given lines are parallel, perpendicular or neitherFind the equation of a line with given propertiesSolve applications of linear equations2.3 Linear EquationsExample: Circle each of the following equations that are linear equations.143y x= +3y x= +6 5y x=- +2y x=-Example: Circle each of the following graphs that are linear.The General Form (or Standard Form) of a linear equation in two variables is any equation in the form: Ax + By = C where A, B, C integers.2.3 Slope Definition and ExamplesThe slope (rate of change) of a line gives the line’s steepness.Examples: Find the indicated slope.1 21 2rise change in run change in y yymx x x-= = =-1 12 2for any two points ( , ) and ( , ) on the linex yx yWe will leave the slope as an improper fraction•from A to B•from B to A•from A to CNote:2.3 Calculating SlopeExamples: Find the slope of the line connecting the points.(3, 7) and (5, 4)(-6, -9) and (-4, 1)Examples: A line passes through the point (-2, -3) and has a slope of -2. Give three additional points on the line.2.3 Calculating SlopeExamples: Find the slope of the line connecting the points.(6, -2) and (-3, -2)(5, -1) and (5, 7)Rule: Rule:2.3 Slope Definition and ExamplesExample: Find the rate of change of the line graphed.Example: Next to each graph, write the letter of the description that best describes the slope. A. PositiveB. NegativeC. Zero D. UndefinedExample: Graph the line that passes through the point (-4, 2) with a slope of2.3 Graphing Using the Slope Example: Graph the line that passes through the point (5, -3) with a slope of -434-Example: Graph the line that passes through the point (-3, -2) with a slope of 02.3 Graphing Using the Slope Example: Graph the line that passes through the point (0, 3) with a slope of undefinedThe Slope-Intercept Form of a linear equation in two variables is any equation in the form: y = mx + b where m is the slope of the line and (0, b) is the coordinate of the y-intercept of the line.2.3 Identify the Slope and y-Intercept of a Linea) What is the slope of the line?b) What is the coordinate of the y-intercept of the line?c) Write the equation of the line in slope-intercept form.2.3 Graph Linear Equations from Slope-Intercept FormExample: Find the slope and the coordinate of the y-intercept of the given linear equation. Graph the equation using that information. 5 3 12x y- =slope:y-int:2.3 Graph Linear Equations from Slope-Intercept FormExample: Find the slope and the coordinate of the y-intercept of the given linear equation. Graph the equation using that information. 6y x=slope:y-int:2.3 Graph Linear Equations from Slope-Intercept FormExample: Find the slope and the coordinate of the y-intercept of the given linear equation. Graph the equation using that information. 2 3 9x y+ =slope:y-int:2.3 Graph Linear Equations from Slope-Intercept FormExample: Find the slope and the coordinate of the y-intercept of the given linear equation. Graph the equation using that information. 4x =-slope:y-int:2.3 Parallel and Perpendicular LinesParallel lines never touch and have equal slopes (but different y-intercepts) 1 2m m=Perpendicular lines meet at a 90 degree angle and have slopes that are negative reciprocals. 121mm=-Example: A given line has a slope of• What is the slope of any line parallel to this line? • What is the slope of any line perpendicular to this line?2.3 Parallel and Perpendicular Lines35m =Examples: Determine if the graphs of the given lines will be parallel, perpendicular or neither?12- 3 and 2 - 9y x x y= =3 - 3 and 3 - 9y x x y= =Recall from sections 3.2, 3.3 and 3.4:2.3 Writing Linear Equations2.3 Writing Linear EquationsThe Slope-Intercept Form of a linear equation in two variables is any equation in the form: y = mx + b where m is the slope of the line and (0, b) is the coordinate of the y-intercept.The Point-Slope Form of a linear equation in two variables is any equation in the form: where m is the slope of the line and is the coordinate of any point on the line.)()(11xxmyy ( )1 1,x yExample:743y x= +Example:1 2( 3)y x- = +What is the slope?What is the coordinate of the y-intercept?What is the slope?What is the coordinate of a point on the line?2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. Slope is ; contains the point (3, 1)122.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. Line contains the points (-3, 4) and (2, 5)2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. x-intercept (-4, 0) and y-intercept (0, 4)2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. Slope is -2 ; contains the point (0, -2)2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. Slope is 0 ; containing the point (3, 8)2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. The y-axis2.3 Writing Linear EquationsExample: Find the equation of the line with the given properties. Express your final answer in slope-intercept form whenever possible. Perpendicular to the line and contains the point (1, -2)0.2 0.5 1x y- =2.3 Solving Applications Involving Linear EquationsHow to Solve a Word Problem:Step 1: Read the problem until you understand it. • What are we asked to find? • What information is given?• What vocabulary is being used?Step