Question
Write an equation of the line passing through the points \( (4,11) \) and \( (-2,-19) \). The equation of the line is \( \square \). (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Ask by Coles Murray. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 5x - 9 \).
Solution
To find the equation of the line passing through the points \( (4, 11) \) and \( (-2, -19) \) in slope-intercept form \( y = mx + b \), follow these steps:
1. **Calculate the slope \( m \):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-19 - 11}{-2 - 4} = \frac{-30}{-6} = 5
\]
2. **Find the y-intercept \( b \):**
Use one of the points to solve for \( b \). Let's use \( (4, 11) \):
\[
11 = 5(4) + b \\
11 = 20 + b \\
b = 11 - 20 \\
b = -9
\]
3. **Write the equation of the line:**
\[
y = 5x - 9
\]
**Final Answer:**
\[
y = 5x - 9
\]
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Simplify this solution Mind Expander
To find the equation of the line passing through the points \( (4,11) \) and \( (-2,-19) \), we first need to calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substituting our points: \[ m = \frac{-19 - 11}{-2 - 4} = \frac{-30}{-6} = 5. \] Now we can use the point-slope form of the line equation: \[ y - y_1 = m(x - x_1). \] Using point \( (4,11) \): \[ y - 11 = 5(x - 4). \] Distributing the 5: \[ y - 11 = 5x - 20. \] Adding 11 to both sides gives us: \[ y = 5x - 9. \] So, the equation of the line is \( y = 5x - 9 \).
