Matemáticas 1 · Tema 7
Pendiente y ordenada al origen
Forma $y = mx + b$
Ejemplo
Escribir la recta $2x+3y-12=0$ en la forma pendiente-ordenada al origen y graficarla.
$2x + 3y - 12 = 0$
$$\begin{aligned} 3y &= -2x + 12 \\ y &= \frac{-2x + 12}{3} \\ \mathbf{y} &\mathbf{= -\tfrac{2}{3}x + 4} \end{aligned}$$$m = -\dfrac{2}{3}$ · $b = 4$
Comprueba que tres puntos de la gráfica cumplen la ecuación $2x+3y-12=0$.
$(0,4)$
$$\begin{aligned}
2(0)+3(4)-12 &= 0 \\
12-12 &= 0 \\
\mathbf{0} &\mathbf{= 0}
\end{aligned}$$
$(6,0)$
$$\begin{aligned}
2(6)+3(0)-12 &= 0 \\
12-12 &= 0 \\
\mathbf{0} &\mathbf{= 0}
\end{aligned}$$
$(3,2)$
$$\begin{aligned}
2(3)+3(2)-12 &= 0 \\
6+6-12 &= 0 \\
\mathbf{0} &\mathbf{= 0}
\end{aligned}$$
Ejercicios
$3x+2y-8=0$
$-4x-3y+9=0$
$5x-2y+4=0$
$4x+3y-6=0$
$5x-4y+12=0$
$-2x-2y+8=0$
$-4x-3y+9=0$
$5x-2y+4=0$
$4x+3y-6=0$
$5x-4y+12=0$
$-2x-2y+8=0$
Ejercicios resueltos
▼$3x + 2y - 8 = 0$
$$\begin{aligned} 2y &= -3x + 8 \\ \mathbf{y} &\mathbf{= -\tfrac{3}{2}x + 4} \end{aligned}$$Comprobación de puntos para $3x+2y-8=0$.
$(0,4)$
$3(0)+2(4)-8=0$$\mathbf{0=0}$
$(2,1)$
$3(2)+2(1)-8=0$$\mathbf{0=0}$
$(1, 2.5)$
$3(1)+2(2.5)-8=0$$\mathbf{0=0}$
$-4x - 3y + 9 = 0$
$$\begin{aligned} -3y &= 4x - 9 \\ \mathbf{y} &\mathbf{= -\tfrac{4}{3}x + 3} \end{aligned}$$Comprobación de puntos para $-4x-3y+9=0$.
$(0,3)$
$-4(0)-3(3)+9=0$$\mathbf{0=0}$
$(3,-1)$
$-4(3)-3(-1)+9=0$$\mathbf{0=0}$
$(1.5, 1)$
$-4(1.5)-3(1)+9=0$$\mathbf{0=0}$
$5x - 2y + 4 = 0$
$$\begin{aligned} -2y &= -5x - 4 \\ \mathbf{y} &\mathbf{= \tfrac{5}{2}x + 2} \end{aligned}$$Comprobación de puntos para $5x-2y+4=0$.
$(0,2)$
$5(0)-2(2)+4=0$$\mathbf{0=0}$
$(2,7)$
$5(2)-2(7)+4=0$$\mathbf{0=0}$
$(-2,-3)$
$5(-2)-2(-3)+4=0$$\mathbf{0=0}$
$4x + 3y - 6 = 0$
$$\begin{aligned} 3y &= -4x + 6 \\ \mathbf{y} &\mathbf{= -\tfrac{4}{3}x + 2} \end{aligned}$$Comprobación de puntos para $4x+3y-6=0$.
$(0,2)$
$4(0)+3(2)-6=0$$\mathbf{0=0}$
$(3,-2)$
$4(3)+3(-2)-6=0$$\mathbf{0=0}$
$(-3,6)$
$4(-3)+3(6)-6=0$$\mathbf{0=0}$
$5x - 4y + 12 = 0$
$$\begin{aligned} -4y &= -5x - 12 \\ \mathbf{y} &\mathbf{= \tfrac{5}{4}x + 3} \end{aligned}$$Comprobación de puntos para $5x-4y+12=0$.
$(0,3)$
$5(0)-4(3)+12=0$$\mathbf{0=0}$
$(4,8)$
$5(4)-4(8)+12=0$$\mathbf{0=0}$
$(-4,-2)$
$5(-4)-4(-2)+12=0$$\mathbf{0=0}$
$-2x - 2y + 8 = 0$
$$\begin{aligned} -2y &= 2x - 8 \\ \mathbf{y} &\mathbf{= -x + 4} \end{aligned}$$Comprobación de puntos para $-2x-2y+8=0$.
$(0,4)$
$-2(0)-2(4)+8=0$$\mathbf{0=0}$
$(4,0)$
$-2(4)-2(0)+8=0$$\mathbf{0=0}$
$(2,2)$
$-2(2)-2(2)+8=0$$\mathbf{0=0}$
Ejercicios extra
▼Bloque A
$3x+2y+4=0$
$-5x+4y-8=0$
$7x-3y+9=0$
$2x-5y-10=0$
$-4x+6y+12=0$
$6x+5y-15=0$
$-3x+8y+16=0$
$4x-7y-21=0$
$5x+3y-9=0$
$-3x-4y+8=0$
$-5x+4y-8=0$
$7x-3y+9=0$
$2x-5y-10=0$
$-4x+6y+12=0$
$6x+5y-15=0$
$-3x+8y+16=0$
$4x-7y-21=0$
$5x+3y-9=0$
$-3x-4y+8=0$
Bloque B
$5x+3y-6=0$
$-2x+9y+18=0$
$5x-10y-20=0$
$3x-7y+14=0$
$-6x+5y+10=0$
$7x+6y-12=0$
$-8x+3y+9=0$
$10x-9y-27=0$
$-5x+4y+20=0$
$3x-2y-6=0$
$-2x+9y+18=0$
$5x-10y-20=0$
$3x-7y+14=0$
$-6x+5y+10=0$
$7x+6y-12=0$
$-8x+3y+9=0$
$10x-9y-27=0$
$-5x+4y+20=0$
$3x-2y-6=0$