Presentation on theme: "Drill #19 Determine the value of r so that a line through the points has the given slope: 1. ( 2 , r ) , ( -1 , 2 ) m = -½ Find the slope of the following."— Presentation transcript:
1 Drill #19Determine the value of r so that a line through the points has the given slope:1. ( 2 , r ) , ( -1 , 2 ) m = -½Find the slope of the following lines. Determine whether they are parallel, perpendicular, or neither:2. y = 3x – x + 2y = 6y = -3x x = 1 – 6y
2 Drill #20 Find the slope intercept form of the following lines: 1. x + 2y = x + ½ y = 93. Find the slope intercept form of the line passing through (1, 3) with a slope of 2.(Write the equation in point-slope for and solve for y.)
3 Drill #21 Identify which of the following lines are parallel: 1. x + 2y = 6 y = - ½x + 24y = 3 – 2x 4x - 8y = -102. Write an equation in slope intercept form parallel to y = 2x – 1 and passing through the point (1, 2).3. Write an equation in slope intercept form perpendicular to 3x – 2y = 3 and passing through the point (3, -2).
4 Drill #23Find the slope of the following lines and then determine which are parallel:1. y = 2x + 3 y – 3 = 3(x + 1)2x – y = 1 3y = 6x + 4y = 3 y = ¾2. Write an equation in slope intercept form parallel toy = ½ x – 1 and passing through the point (4, 6).3. Write an equation in slope intercept form perpendicular to y = ½ x – 1 and passing through the point (4, 6).
5 2-4 Writing Linear Equations Objective: To write an equation of a line in slope intercept form given the slope and one or two points, and to write an equation of a line that is parallel or perpendicular to the graph of a given equation.
6 Slope-Intercept Form Definition: An equation in the form of y = mx + b where m = slope and b = y- interceptIn order to write an equation in slope-intercept form you need to know the slope (m) and the y- intercept (b)
7 Classwork Use the Standard Form formulas: Y-intercept = C/B Slope = -A/BTo complete2-4 Practice #1-4
9 Writing Equations in Slope Intercept Form* Write the equation of the line with given slope and y- intercepts:Ex1: m = 5 b = ¾1A: m = b =1B: m = 0 b = 0
10 Point Slope Form * Point Slope Form: An equation in the form of where Are the coordinates of a point on the line and m is the slope of the line.NOTE: For point slope form we need a point and the slope (or two points).
11 Point Slope ExamplesFind the equation of the line (in point-slope form):Ex2. m = 2 and passes through (2, -3)2A. m = ½ and passes through (-2, 5)
12 Find the Equation of a Line in Slope Intercept Form* Passing through a point (x1, y1) with slope m:Method 1:1. Substitute the point (x1, y1) and the slope m into the formula y = mx + b2. Solve for b.3. Substitute m and b into y = mx + b formulaMethod 2:1. Write the equation in Point Slope form.2. Solve for y
13 Finding the equation of a line Find the slope-intercept form of a line that has a slope of and passes through (-6, 1).m = ?b = ?Method 1Substitute m into the equation y = mx + b.Substitute (-6, 1) for x and y in the equation.Solve for b.Once you know m and b you can put the equation in slope-intercept form.
14 Method 2: Point Slope to Slope Intecept Convert the point-slope equation into slope-intercept.To convert to slope-intercept form, solve the equation for y.
16 Write the Equation of a Parallel or Perpendicular Line* 1st Determine the slope of the line.If finding a parallel line use the same slope as the lineIf finding a perpendicular line use the negative reciprocal slope2nd Write the equation in Point Slope form3rd Convert to Standard or Slope-Intercept Form
17 Find the equation of the line* EXAMPLE 1 That passes through (-9, 5) and is perpendicular to the line whose equation isy = -3x + 2Find the perpendicular slopeUse the point (point- slope form) to find the equation of the line
18 Parallel/Perpendicular Examples Find the equation of the line (in slope-intercept form):1A. Parallel to y = 3x – 1 and passes through (2, -3)1B. Perpendicular to 2x – y = 10 and passing through (-1, -2)