Reed Mcguire
03/31/2024 · Senior High School
Determinar la reda que pasa pod \( (-4,3) \) y \( (1,5) \)
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Step-by-step Solution
Para determinar la ecuación de la recta que pasa por los puntos \((-4, 3)\) y \((1, 5)\), primero necesitamos calcular la pendiente \(m\) de la recta utilizando la fórmula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Donde \((x_1, y_1) = (-4, 3)\) y \((x_2, y_2) = (1, 5)\).
Sustituyendo los valores:
\[
m = \frac{5 - 3}{1 - (-4)} = \frac{2}{1 + 4} = \frac{2}{5}
\]
Ahora que tenemos la pendiente \(m = \frac{2}{5}\), podemos usar la forma punto-pendiente de la ecuación de la recta, que es:
\[
y - y_1 = m(x - x_1)
\]
Usando el punto \((-4, 3)\):
\[
y - 3 = \frac{2}{5}(x + 4)
\]
Ahora, simplificamos la ecuación:
\[
y - 3 = \frac{2}{5}x + \frac{2}{5} \cdot 4
\]
\[
y - 3 = \frac{2}{5}x + \frac{8}{5}
\]
\[
y = \frac{2}{5}x + \frac{8}{5} + 3
\]
Para sumar \(3\) (que es \(\frac{15}{5}\)):
\[
y = \frac{2}{5}x + \frac{8}{5} + \frac{15}{5}
\]
\[
y = \frac{2}{5}x + \frac{23}{5}
\]
Por lo tanto, la ecuación de la recta que pasa por los puntos \((-4, 3)\) y \((1, 5)\) es:
\[
y = \frac{2}{5}x + \frac{23}{5}
\]
Quick Answer
La ecuación de la recta es \( y = \frac{2}{5}x + \frac{23}{5} \).
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