drill #19 determine the value of r so that a line through the points has the given slope: 1.( 2, r...
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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 lines. Determine whether they are parallel, perpendicular, or neither:
2. y = 3x – 4 3. 3x + 2y = 6y = -3x + 1 4x = 1 – 6y
Drill #20
Find the slope intercept form of the following lines:
1. x + 2y = 6 2. 3x + ½ y = 9
3. 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.)
Drill #21Identify which of the following lines are parallel:1. x + 2y = 6 y = - ½x + 2 4y = 3 – 2x 4x - 8y = -10
2. 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).
Drill #23
Find 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 = ¾
2. Write an equation in slope intercept form parallel to y = 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).
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.
Slope-Intercept Form
Definition: An equation in the form of
y = mx + b
where m = slope and b = y- intercept
In order to write an equation in slope-intercept form you need to know the slope (m) and the y- intercept (b)
Classwork
Use the Standard Form formulas:
Y-intercept = C/B
Slope = -A/B
To complete
2-4 Practice #1-4
Classwork
2-4 Practice
#9 – 17 (ODD)
Writing Equations in Slope Intercept Form*
Write the equation of the line with given slope and y- intercepts:
Ex1: m = 5 b = ¾
1A: m = b =
1B: m = 0 b = 0
9
5
13
6
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 xxmyy ),( 11 yx
Point Slope Examples
Find 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)
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 + b
2. Solve for b.
3. Substitute m and b into y = mx + b formula
Method 2:
1. Write the equation in Point Slope form.
2. Solve for y
Finding the equation of a lineFind the slope-intercept form of a line that has a
slope of and passes through (-6, 1).
m = ?b = ?Method 1• Substitute 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.
3
2
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.
Classwork
2-4 Practice
#9 – 17 (ODD)
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 line
• If finding a perpendicular line use the negative reciprocal slope
2nd Write the equation in Point Slope form
3rd Convert to Standard or Slope-Intercept Form
Find the equation of the line*EXAMPLE 1
That passes through (-9, 5) and is perpendicular to the line whose equation is
y = -3x + 2
• Find the perpendicular slope
• Use the point (point- slope form) to find the equation of the line
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)
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