Question

a line has a slope of $-\frac{1}{10}$ and passes through the point $(10, 7)$. what is its equation in point - slope form?\
use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.\
$y - \square = \square (x - \square)$

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point that the line passes through.

Step2: Identify \(m\), \(x_1\) and \(y_1\)

We are given that the slope \(m =-\frac{1}{10}\) and the line passes through the point \((10,7)\). So, \(x_1 = 10\) and \(y_1=7\).

Step3: Substitute into point - slope form

Substituting \(m =-\frac{1}{10}\), \(x_1 = 10\) and \(y_1 = 7\) into the point - slope form \(y - y_1=m(x - x_1)\), we get \(y - 7=-\frac{1}{10}(x - 10)\).

Answer:

\(y - \boldsymbol{7}=\boldsymbol{-\frac{1}{10}}(x - \boldsymbol{10})\)