Question
If \( (-2,11) \) and \( (9,22) \) are two anchor points on a trend line, then find the equation of the line. \[ y=x+[?] \]
Ask by Turner Long. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
La ecuación de la recta es \( y = x + 13 \).
Solution
Para encontrar la ecuación de la recta que pasa por los puntos \((-2, 11)\) y \((9, 22)\), seguimos estos pasos:
1. **Calcular la pendiente (m):**
\[
m = \frac{22 - 11}{9 - (-2)} = \frac{11}{11} = 1
\]
2. **Usar la forma de la ecuación de la recta \( y = mx + b \) para encontrar \( b \):**
Utilizando el punto \((-2, 11)\):
\[
11 = (1)(-2) + b \\
11 = -2 + b \\
b = 13
\]
3. **Escribir la ecuación de la recta:**
\[
y = x + 13
\]
Por lo tanto, la ecuación de la recta es:
\[
y = x + 13
\]
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Simplify this solution Mind Expander
To find the equation of the line passing through the points \((-2,11)\) and \((9,22)\), we first calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\): \[ m = \frac{22 - 11}{9 - (-2)} = \frac{11}{11} = 1. \] With the slope \(m = 1\), we can use the point-slope form of the equation, which is \(y - y_1 = m(x - x_1)\). Taking the point \((-2, 11)\): \[ y - 11 = 1(x + 2) \implies y - 11 = x + 2 \implies y = x + 13. \] So, the equation of the line is: \[ y = x + [13]. \]
