Question
A line includes the points \( (-5,-6) \) and \( (-6,-4) \). What is its equation in point-slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Ask by Chambers Frank. in the United States
Jan 31,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line in point-slope form is \( y + 6 = -2(x + 5) \).
Solution
To find the equation of the line in point-slope form that passes through the points \((-5, -6)\) and \((-6, -4)\), follow these steps:
1. **Calculate the slope (\(m\))**:
The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the given points:
\[
m = \frac{-4 - (-6)}{-6 - (-5)} = \frac{2}{-1} = -2
\]
2. **Choose one of the points**:
Let's use the point \((-5, -6)\).
3. **Write the point-slope form**:
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Substituting the values:
\[
y - (-6) = -2(x - (-5))
\]
\[
y + 6 = -2(x + 5)
\]
So, the equation of the line in point-slope form is:
\[
\boxed{y + 6 = -2\, (x + 5)}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the equation of the line in point-slope form, we first need to calculate the slope of the line that passes through the points \( (-5,-6) \) and \( (-6,-4) \). The slope \( m \) is calculated as follows: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-6)}{-6 - (-5)} = \frac{-4 + 6}{-6 + 5} = \frac{2}{-1} = -2 \] Now with the slope \( m = -2 \) and using one of the points, let's use \( (-5, -6) \), we can write the equation in point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting the values, we get: \[ y - (-6) = -2(x - (-5)) \] This simplifies to: \[ y + 6 = -2(x + 5) \] Hence, the equation of the line in point-slope form is: \[ y + 6 = -2(x + 5) \]
