$$ (2, n) $$ and $$ (0,8) $$ Slope $$ =-2 $$ $$ \mathrm{n}= $$ $$ \qquad $$ $$ (\mathrm{g}, 6) $$ and ( $$ -5,-9 $$ ) Slope $$ =\frac{3}{2} $$ $$ \mathrm{g}= $$ $$ \qquad $$ $$ (1,-1) $$ and $$ (-5, z) $$ Slope $$ =-\frac{4}{3} $$ 4) $$ (5,4) $$ and $$ (10, c) $$ Slope $$ =-\frac{2}{5} $$ $$ \mathrm{c}= $$ $$ \qquad $$ 6) $$ (1, h) $$ and $$ (4,8) $$ Slope $$ =1 $$ $$ \mathrm{h}= $$ $$ \qquad $$ 8) $$ (s,-7) $$ and $$ (3,-10) $$ Slope $$ =-\frac{1}{2} $$

Question

UpStudy AI · Accepted Answer

**1) Determinar $$ n $$ para los puntos $$ (2,n) $$ y $$ (0,8) $$ con pendiente $$ -2 $$.**

La fórmula de la pendiente es
$$
m = \frac{y_2 - y_1}{x_2 - x_1}.
$$
Asignamos: $$ P_1 = (2, n) $$ y $$ P_2 = (0, 8) $$. Entonces,
$$
-2 = \frac{8 - n}{0 - 2} = \frac{8 - n}{-2}.
$$
Multiplicamos ambos lados por $$-2$$:
$$
8 - n = (-2)(-2) = 4.
$$
Despejamos $$ n $$:
$$
n = 8 - 4 = 4.
$$

---

**2) Determinar $$ g $$ para los puntos $$ (g,6) $$ y $$ (-5,-9) $$ con pendiente $$\frac{3}{2}$$.**

Con la fórmula de la pendiente:
$$
\frac{3}{2} = \frac{-9-6}{-5-g} = \frac{-15}{-5-g}.
$$
Multiplicamos cruzado:
$$
-15 \cdot 2 = 3(-5-g),
$$
$$
-30 = -15 - 3g.
$$
Sumamos $$ 15 $$ a ambos lados:
$$
-15 = -3g,
$$
$$
g = \frac{-15}{-3} = 5.
$$

---

**3) Determinar $$ z $$ para los puntos $$ (1,-1) $$ y $$ (-5,z) $$ con pendiente $$-\frac{4}{3}$$.**

Aplicamos la fórmula:
$$
-\frac{4}{3} = \frac{z - (-1)}{-5 - 1} = \frac{z + 1}{-6}.
$$
Multiplicamos ambos lados por $$-6$$:
$$
z + 1 = \left(-\frac{4}{3}\right)(-6) = \frac{24}{3} = 8.
$$
De donde:
$$
z = 8 - 1 = 7.
$$

---

**4) Determinar $$ c $$ para los puntos $$ (5,4) $$ y $$ (10,c) $$ con pendiente $$-\frac{2}{5}$$.**

Utilizando la fórmula de la pendiente:
$$
-\frac{2}{5} = \frac{c - 4}{10 - 5} = \frac{c - 4}{5}.
$$
Multiplicamos ambos lados por $$5$$:
$$
c - 4 = -2,
$$
$$
c = 4 - 2 = 2.
$$

---

**6) Determinar $$ h $$ para los puntos $$ (1,h) $$ y $$ (4,8) $$ con pendiente $$ 1 $$.**

La pendiente es
$$
1 = \frac{8-h}{4-1} = \frac{8-h}{3}.
$$
Multiplicamos por $$3$$:
$$
8 - h = 3,
$$
$$
h = 8 - 3 = 5.
$$

---

**8) Determinar $$ s $$ para los puntos $$ (s,-7) $$ y $$ (3,-10) $$ con pendiente $$-\frac{1}{2}$$.**

La pendiente se calcula como:
$$
-\frac{1}{2} = \frac{-10 - (-7)}{3-s} = \frac{-3}{3-s}.
$$
Multiplicamos cruzado:
$$
-3 \cdot 2 = -1 (3-s),
$$
$$
-6 = -3 + s.
$$
Sumamos $$ 3 $$ a ambos lados:
$$
-3 = s,
$$
$$
s = -3.
$$
1) $$ n = 4 $$ 2) $$ g = 5 $$ 3) $$ z = 7 $$ 4) $$ c = 2 $$ 6) $$ h = 5 $$ 8) $$ s = -3 $$

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