Question
Find the point-slope equation for the line that passes through the points \( (15,10) \) and \( (16,15) \). Use the first point in your equation. \( y-[?]=[](x-[]) \)
Ask by French Reeves. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
La ecuación punto-pendiente es \( y - 10 = 5(x - 15) \).
Solution
Para encontrar la ecuación punto-pendiente de la recta que pasa por los puntos \((15, 10)\) y \((16, 15)\), seguimos los siguientes pasos:
1. **Calcular la pendiente (m):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 10}{16 - 15} = \frac{5}{1} = 5
\]
2. **Usar la forma punto-pendiente** con el primer punto \((15, 10)\):
\[
y - y_1 = m(x - x_1)
\]
Sustituyendo los valores:
\[
y - 10 = 5(x - 15)
\]
**Ecuación final:**
\[
y - 10 = 5(x - 15)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the point-slope equation of the line passing through the points \( (15,10) \) and \( (16,15) \), we first need to calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the values, we get: \[ m = \frac{15 - 10}{16 - 15} = \frac{5}{1} = 5 \] Now, using the point-slope formula: \[ y - y_1 = m(x - x_1) \] With \( (x_1, y_1) = (15, 10) \), our equation becomes: \[ y - 10 = 5(x - 15) \] So, the point-slope equation you are looking for is: \[ y - 10 = 5(x - 15) \] This equation perfectly describes the line passing through the given points! Enjoy graphing it!
