5.5 b standard and point slope form
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5.5 Standard and Point-Slope Forms B
5.5 Standard and Point-Slope Forms B
5.5 Practice5.5 Practice
Write each equation in Standard Form.Standard Form: Ax + By = C
Write each equation in Standard Form.Standard Form: Ax + By = C
1. 7x + 2y - 11 = 01. 7x + 2y - 11 = 0
+11 +11+11 +11
7x + 2y = 117x + 2y = 11
Write each equation in Standard Form.Standard Form: Ax + By = C
Write each equation in Standard Form.Standard Form: Ax + By = C
2. 4x = 8y + 102. 4x = 8y + 10-8y -8y-8y -8y
4x - 8y = 104x - 8y = 10
Write each equation in Standard Form.Standard Form: Ax + By = C
Write each equation in Standard Form.Standard Form: Ax + By = C
3. -12x + 2 = 17y - 33. -12x + 2 = 17y - 3-17y -17y-17y -17y
-12x - 17y + 2 = -3-12x - 17y + 2 = -3
-2 -2-2 -2
-12x - 17y = -5-12x - 17y = -5
Write each equation in Standard Form.Standard Form: Ax + By = C
Write each equation in Standard Form.Standard Form: Ax + By = C
4. 4y = 2x - 84. 4y = 2x - 8-2x - 2x-2x - 2x
-2x + 4y = -8-2x + 4y = -8
Write an equation in point-slope form for the line that has the given slope and the given point.
Write an equation in point-slope form for the line that has the given slope and the given point.
5. Slope 3/4, (4, 6)5. Slope 3/4, (4, 6)
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _6__ = _3/4_(x - _4_ )y - _6__ = _3/4_(x - _4_ )
Write an equation in point-slope form for the line that has the given slope and the given point.
Write an equation in point-slope form for the line that has the given slope and the given point.
6. Slope -2, (3, 4)6. Slope -2, (3, 4)
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _4__ = _-2_(x - _3_ )y - _4__ = _-2_(x - _3_ )
Write an equation in point-slope form for the line that has the given slope and the given point.
Write an equation in point-slope form for the line that has the given slope and the given point.
7. Slope: -3, (-4, 8)7. Slope: -3, (-4, 8)
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _8__ = _-3_(x - _-4_ )y - _8__ = _-3_(x - _-4_ )
y - _8_ = _-3_ (x + 4_)y - _8_ = _-3_ (x + 4_)
Write an equation in point-slope form for the line that has the given slope and the given point.
Write an equation in point-slope form for the line that has the given slope and the given point.
8. Slope 1/5, (7, -3)8. Slope 1/5, (7, -3)
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _-3__ = _1/5_(x - _7_ )y - _-3__ = _1/5_(x - _7_ )
y + 3_ = _1/5_ (x - 7_)y + 3_ = _1/5_ (x - 7_)
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.9. (-3, 3), (-4, 4)
Step 1: Identify Slope & Pts
9. (-3, 3), (-4, 4)
Step 1: Identify Slope & Pts
slope =rise = y2 – y1 =
run x2 – x1
4 - 3 =-4 - (-3)
x1, y1 x2, y2
1 =-1
-1
9. (-3, 3); m = -19. (-3, 3); m = -1
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _3__ = _-1_(x - _-3_ )y - _3__ = _-1_(x - _-3_ )
Y - 3 = -1 (x + 3 )Y - 3 = -1 (x + 3 )
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
9. Y-intercept (x=0)9. Y-intercept (x=0)
Y - 3 = -1 (x + 3 )Y - 3 = -1 (x + 3 )
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Y - 3 = -1 (0 + 3 )Y - 3 = -1 (0 + 3 )
Y - 3 = -1 (3)Y - 3 = -1 (3)
Y - 3 = -3Y - 3 = -3Y + 3 = +3Y + 3 = +3
Y = 0Y = 0
9. Slope-intercept Form9. Slope-intercept Form
Y = mx + bY = mx + b
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
M = -1M = -1
B = 0B = 0
Y = -1x + 0Y = -1x + 0
Y = -xY = -x
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.10. (5, 2), (-2, 5)
Step 1: Identify Slope & Pts
10. (5, 2), (-2, 5)
Step 1: Identify Slope & Pts
slope =rise = y2 – y1 =
run x2 – x1
5 - 2 =-2 - 5
x1, y1 x2, y2
3 -7
9. (5, 2); m = -3/79. (5, 2); m = -3/7
y - ____ = ____(x - ___ )y - ____ = ____(x - ___ )
y - y1 = m(x - x1 )y - y1 = m(x - x1 )
y - _2__ = _-3/7_(x - _5_ )y - _2__ = _-3/7_(x - _5_ )
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
10. Y-intercept (x=0)10. Y-intercept (x=0)
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Y - 2 = -3/7 (0 - 5 )Y - 2 = -3/7 (0 - 5 )
Y - 2 = -3/7 (-5)Y - 2 = -3/7 (-5)
Y - 2 = 15/7Y - 2 = 15/7Y + 2 = + 2Y + 2 = + 2
Y = 29/7 = 4 and 1/7Y = 29/7 = 4 and 1/7
y - _2__ = _-3/7_(x - _5_ )y - _2__ = _-3/7_(x - _5_ )
10. Slope-intercept Form10. Slope-intercept Form
Y = mx + bY = mx + b
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
Use each pair of points to write the equation of a line in point-slope form and slope-intercept
form.
M = -3/7M = -3/7
B = 29/7B = 29/7
Y = -3/7x + 29/7Y = -3/7x + 29/7
Find the x and y intercepts, and use them to graph the equation.Find the x and y intercepts, and use them to graph the equation.11. 2x - y = -411. 2x - y = -4
X -intercept - 0 for y
2x - 0 = -42x = -4 (-2, 0)
0 - y = -4
2(0) - y = -4 Y-intercept - 0 for x
-y = -4 (0, 4)
X = -2
y = 4
Find the x and y intercepts, and use them to graph the equation.Find the x and y intercepts, and use them to graph the equation.
(-2, 0) and (0, 4)(-2, 0) and (0, 4)
x
y
Find the x and y intercepts, and use them to graph the equation.Find the x and y intercepts, and use them to graph the equation.12. X - 2y = 212. X - 2y = 2
X -intercept - 0 for y
X - 2(0) = 2X - 0 = 2 (2, 0)
- 2y = 2
0 - 2y = 2 Y-intercept - 0 for x
Y = -1 (0, -1)
X = 2
Find the x and y intercepts, and use them to graph the equation.Find the x and y intercepts, and use them to graph the equation.
(2, 0) and (0, -1)(2, 0) and (0, -1)
x
y12.12.