Algebra 1 SOL A.6 Standard Form, Parallel/Perpendicular Lines WS
Mrs. Grieser
Name: ________________________________________ Date: __________________ Block: _______
Standard Form: Ax + By = C
Writing Parallel Lines
Use properties of equality to put linear
equations in standard form


“Best” standard form:
 Coefficients are integers
 Greatest common factor among
coefficients is 1
 Leading coefficient (A) is positive

Ex: Write y = -2x + 1 in standard form:
2x + y = 1
Writing Horizontal and Vertical Lines


Horizontal lines are of the form y=a
Vertical lines are of the form x = b
Write the equation of the vertical and
horizontal lines that pass through point
(-1, 5)

y = 5 (horizontal); x = -1 (vertical)
Have SAME slope
Ex: Write line parallel to y = 4x – 3 and
passes through (-1, 2)
o m = 4 (same slope!)
o Use point-slope
 y – 2 = 4(x + 1)
 y = 4x + 6
Writing Perpendicular Lines


Slopes are NEGATIVE RECIPROCALS
Ex: Write line perpendicular to y = 2x + 3
and passes through (4, 1)
1
o m =  (negative reciprocal of 2)
2
o Use point-slope
1
 y – 1 =  (x - 4)
2
1
 y=  x+3
2
Exercises:
1) Write two equations in standard form that are equivalent to the given equation.
a) 6x + 24y = 18
b) -4x – 2y = 16
2) Write an equation of the line in standard form that passes through the given point and
has the given slope.
a)
(4, 3); m = 7
b) (-2, 6); m = 1
c) (-15, -4); m =
1
2
3) Write an equation of the line in standard form that passes through the given points.
a)
(2, 6), (3, 8)
b) (3, -8), (5, -9)
c) (-3, -1), (6, -8)
4) Write an equation of the horizontal and vertical lines that pass through the given point.
a)
(-2, 6)
horizontal ___________ vertical ____________
b) (5, -5)
horizontal ___________ vertical ____________
Algebra 1 SOL A.6 Standard Form, Parallel/Perpendicular Lines WS
Mrs. Grieser
5) Write an equation of the line, in standard form, that passes through the given point and
is parallel to the given line.
a)
y = 5x – 3; (4, 7)
b) 3y = 2x + 3; (3, -2)
c) 8x + 4y = 5; (0, -8)
6) Write an equation of the line, in standard form, that passes through the given point and
is perpendicular to the given line.
a)
y=-
1
5
x + 1; (3, -7)
b) y =
2
x – 4; (6, 0)
3
c) 8x + 3y = 7; (-4, -8)
7) Determine which of the following lines, if any, are parallel or perpendicular.
Line a: y = -2x + 5;
Line b: 2y – x = 3;
Line c: 2x + y = 1
8) A model of a kite design is shown on the graph:
a) Write an equation that models line A of the kite.
b) Write an equation that models line B of the kite.
c) Do the kite parts form a right angle (a right angle
measures 90o)? Explain your answer.