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Matemáticas 1 · Tema 6

Gráfica con tabulación

Videos

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Ejemplo

Ecuación original: 4x+2y=64x + 2y = 6

Despeje de yy:

2y=6−4x2y = 6 - 4x
y=6−4x2y = \dfrac{6 - 4x}{2}
y=3−2x\mathbf{y = 3 - 2x}

Tabulación y procedimiento:

XY
−27
−15
03
11
2−1
y=3−2(x)y = 3 - 2(x)
3−2(−2)=3+4=3-2(-2) = 3+4 = 77
3−2(−1)=3+2=3-2(-1) = 3+2 = 55
3−2(0)=3+0=3-2(0) = 3+0 = 33
3−2(1)=3−2=3-2(1) = 3-2 = 11
3−2(2)=3−4=3-2(2) = 3-4 = −1-1
x y

Ejercicios

Bloque 1
6x+2y=106x+2y=10
12x+4y=812x+4y=8
15x+3y=915x+3y=9
Bloque 2
−6x+3y=9-6x+3y=9
8x−2y=48x-2y=4
−5x+5y=15-5x+5y=15

Respuestas

▼

Ecuación original: 6x+2y=106x + 2y = 10

Despeje de yy:

2y=10−6x2y = 10 - 6x
y=10−6x2y = \dfrac{10 - 6x}{2}
y=5−3x\mathbf{y = 5 - 3x}

Tabulación y procedimiento:

XY
−211
−18
05
12
2−1
y=5−3(x)y = 5 - 3(x)
5−3(−2)=5+6=5-3(-2) = 5+6 = 1111
5−3(−1)=5+3=5-3(-1) = 5+3 = 88
5−3(0)=5+0=5-3(0) = 5+0 = 55
5−3(1)=5−3=5-3(1) = 5-3 = 22
5−3(2)=5−6=5-3(2) = 5-6 = −1-1
x y

Ecuación original: 12x+4y=812x + 4y = 8

Despeje de yy:

4y=8−12x4y = 8 - 12x
y=8−12x4y = \dfrac{8 - 12x}{4}
y=2−3x\mathbf{y = 2 - 3x}

Tabulación y procedimiento:

XY
−28
−15
02
1−1
2−4
y=2−3(x)y = 2 - 3(x)
2−3(−2)=2+6=2-3(-2) = 2+6 = 88
2−3(−1)=2+3=2-3(-1) = 2+3 = 55
2−3(0)=2+0=2-3(0) = 2+0 = 22
2−3(1)=2−3=2-3(1) = 2-3 = −1-1
2−3(2)=2−6=2-3(2) = 2-6 = −4-4
x y

Ecuación original: 15x+3y=915x + 3y = 9

Despeje de yy:

3y=9−15x3y = 9 - 15x
y=9−15x3y = \dfrac{9 - 15x}{3}
y=3−5x\mathbf{y = 3 - 5x}

Tabulación y procedimiento:

XY
−213
−18
03
1−2
2−7
y=3−5(x)y = 3 - 5(x)
3−5(−2)=3+10=3-5(-2) = 3+10 = 1313
3−5(−1)=3+5=3-5(-1) = 3+5 = 88
3−5(0)=3+0=3-5(0) = 3+0 = 33
3−5(1)=3−5=3-5(1) = 3-5 = −2-2
3−5(2)=3−10=3-5(2) = 3-10 = −7-7
x y

Ecuación original: −6x+3y=9-6x + 3y = 9

Despeje de yy:

3y=9+6x3y = 9 + 6x
y=9+6x3y = \dfrac{9 + 6x}{3}
y=3+2x\mathbf{y = 3 + 2x}

Tabulación y procedimiento:

XY
−2−1
−11
03
15
27
y=3+2(x)y = 3 + 2(x)
3+2(−2)=3−4=3+2(-2) = 3-4 = −1-1
3+2(−1)=3−2=3+2(-1) = 3-2 = 11
3+2(0)=3+0=3+2(0) = 3+0 = 33
3+2(1)=3+2=3+2(1) = 3+2 = 55
3+2(2)=3+4=3+2(2) = 3+4 = 77
x y

Ecuación original: 8x−2y=48x - 2y = 4

Despeje de yy:

−2y=4−8x-2y = 4 - 8x
y=4−8x−2y = \dfrac{4 - 8x}{-2}
y=−2+4x\mathbf{y = -2 + 4x}

Tabulación y procedimiento:

XY
−2−10
−1−6
0−2
12
26
y=−2+4(x)y = -2 + 4(x)
−2+4(−2)=−2−8=-2+4(-2) = -2-8 = −10-10
−2+4(−1)=−2−4=-2+4(-1) = -2-4 = −6-6
−2+4(0)=−2+0=-2+4(0) = -2+0 = −2-2
−2+4(1)=−2+4=-2+4(1) = -2+4 = 22
−2+4(2)=−2+8=-2+4(2) = -2+8 = 66
x y

Ecuación original: −5x+5y=15-5x + 5y = 15

Despeje de yy:

5y=15+5x5y = 15 + 5x
y=15+5x5y = \dfrac{15 + 5x}{5}
y=3+x\mathbf{y = 3 + x}

Tabulación y procedimiento:

XY
−21
−12
03
14
25
y=3+(x)y = 3 + (x)
3+(−2)=3−2=3+(-2) = 3-2 = 11
3+(−1)=3−1=3+(-1) = 3-1 = 22
3+(0)=3+0=3+(0) = 3+0 = 33
3+(1)=3+1=3+(1) = 3+1 = 44
3+(2)=3+2=3+(2) = 3+2 = 55
x y

Ejercicios extra 1

▼
Bloque A
−12x−3y=6-12x-3y=6
3x+y=93x+y=9
10x+5y=2010x+5y=20
Bloque B
6x−3y=126x-3y=12
−3x+y=−5-3x+y=-5
4x−y=84x-y=8

Ejercicios extra 2

▼
Bloque 1
−8x+4y=−16-8x+4y=-16
−4x+2y=8-4x+2y=8
6x+3y=−126x+3y=-12
2x+y=42x+y=4
15x−5y=1015x-5y=10
4x−2y=104x-2y=10
−6x−2y=−14-6x-2y=-14
Bloque 2
−10x+2y=−12-10x+2y=-12
8x+4y=248x+4y=24
−5x+2y=−10-5x+2y=-10
9x−3y=189x-3y=18
−2x−y=−4-2x-y=-4
12x+6y=3012x+6y=30
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