Question

there is a line that includes the point (10, 1) and has a slope of $-\frac{1}{5}$. 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 \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

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

We are given that the line passes through the point \((10,1)\), so \(x_1 = 10\) and \(y_1=1\). The slope \(m=-\frac{1}{5}\).

Step3: Substitute into point - slope form

Substitute \(y_1 = 1\), \(m=-\frac{1}{5}\) and \(x_1 = 10\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y - 1=-\frac{1}{5}(x - 10)\).

Answer:

\(y - \boldsymbol{1}=\boldsymbol{-\frac{1}{5}}(x - \boldsymbol{10})\)