Question

the points (7, -3) and (-5, -1) fall on a particular line. 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.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(7, - 3)\) and \((x_2, y_2)=(-5, - 1)\). Then \( m=\frac{-1-(-3)}{-5 - 7}=\frac{-1 + 3}{-12}=\frac{2}{-12}=-\frac{1}{6} \).

Step2: Write the point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((7,-3)\) (we could also use \((-5,-1)\)). Substituting \( m =-\frac{1}{6}\), \(x_1 = 7\) and \(y_1=-3\) into the point - slope formula, we get \( y-(-3)=-\frac{1}{6}(x - 7) \), which simplifies to \( y + 3=-\frac{1}{6}(x - 7) \). If we use the point \((-5,-1)\), substituting \( m=-\frac{1}{6}\), \(x_1=-5\) and \(y_1 = - 1\) into the formula, we get \( y-(-1)=-\frac{1}{6}(x-(-5)) \), or \( y + 1=-\frac{1}{6}(x + 5) \).

Answer:

\( y + 3=-\frac{1}{6}(x - 7) \) (or \( y + 1=-\frac{1}{6}(x + 5) \))