Question

a line includes the points (8, -8) and (6, -7). 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(8, - 8)\) and \((x_2,y_2)=(6, - 7)\). So, \( m=\frac{-7-(-8)}{6 - 8}=\frac{-7 + 8}{-2}=\frac{1}{-2}=-\frac{1}{2} \).

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 \((8,-8)\) (we could also use \((6, - 7)\)). Substituting \( m =-\frac{1}{2}\), \( x_1 = 8\) and \( y_1=-8\) into the point - slope formula, we get \( y-(-8)=-\frac{1}{2}(x - 8) \), which simplifies to \( y + 8=-\frac{1}{2}(x - 8) \). If we use the point \((6,-7)\), substituting \( m =-\frac{1}{2}\), \( x_1 = 6\) and \( y_1=-7\) into the formula, we get \( y-(-7)=-\frac{1}{2}(x - 6) \), or \( y + 7=-\frac{1}{2}(x - 6) \).

Answer:

\( y + 8=-\frac{1}{2}(x - 8) \) (or \( y + 7=-\frac{1}{2}(x - 6) \))