4ESO mathematics B
IES Montevil
unit 4: algebra
curso 2011/2012
CLASS EXERCISE 11: Drawing algebraic expressions (solutions)
1. Grade 1 expressions
a ⋅ x + b ⋅ y = c and y = m ⋅ x + n
expression
3x + y = 2
y = -3x + 2
y = 2x - 5
2x - y = 5
-6x + 2y = 1
y = 3x + 1/2
y = -3x - 5
3x + y = -5
x - 2y = 0
y = x/2
session 3!
LA CASA DE EVARISTO NOETHER
parameters
type of line
a = 3, b = 1, c = 2
m = −3, n = 2
m = 2, n = −5
a = 2, b = −1, c = 5
a = −6, b = 2, c = 1
m = 3, n =
1
2
m = −3, n = −5
In every case the
geometrical representation
of the equations is a
straight line. Depending
on the value of the
parameters we have
different types of straight
lines
a = 3, b = 1, c = −5
a = 1, b = −2, c = 0
m = 21 , n = 0
1!
solutions
http://blog.educastur.es/rubenzamanillo/
4ESO mathematics B
IES Montevil
unit 4: algebra
curso 2011/2012
2. Grade 2 expressions (I)
y = A ⋅ x2 + B ⋅ x + C
expression
parameters
y = x 2 + x − 12
A = 1, B = 1, C = −12
y = −2x 2 + 18
A = −2, B = 0, C = 18
y = 3x 2 + 3x − 6
A = 3, B = 3, C = −6
y = 2x 2 − 5x
A = 2, B = −5, C = 0
type of line
All of them are
parabolas
3. Grade 2 expressions (II)
A ⋅ x 2 + B ⋅ y 2 + C ⋅ xy + D ⋅ x + E ⋅ y + F = 0
type
of line
expression
parameters
x + y − 16 = 0
A = 1, B = 1, C = 0,
D = 0, E = 0, F = −16
2
2
3x + 3y − 5x + 7y = 10
2
2
x + 4y − 9x + 7y + 1= 0
2
2
x 2 − 2y 2 + 5xy + 4 = 0
y + 7x − y + 3 = 0
2
session 3!
LA CASA DE EVARISTO NOETHER
A = 3, B = 3, C = 0,
circum
ference
D = −5, E = 7, F = −10
A = 1, B = 4, C = 0,
D = −9, E = 7, F = 1
A = 1, B = −2, C = 5,
D = 0, E = 0, F = 4
A = 0, B = 1, C = 0,
D = 7, E = −1, F = 3
2!
ellipse
hyperbola
parabola
solutions
http://blog.educastur.es/rubenzamanillo/
4ESO mathematics B
IES Montevil
unit 4: algebra
session 3!
LA CASA DE EVARISTO NOETHER
curso 2011/2012
3!
solutions
http://blog.educastur.es/rubenzamanillo/