Question

a line has a slope of $-\frac{5}{7}$ and passes through the point (3, 1). 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.

Explanation:

Step1: Recall point - slope formula

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 values of \(m\), \(x_1\) and \(y_1\)

We are given that the slope \(m =-\frac{5}{7}\) and the point \((x_1,y_1)=(3,1)\).

Step3: Substitute values into the formula

Substitute \(m =-\frac{5}{7}\), \(x_1 = 3\) and \(y_1=1\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 1=-\frac{5}{7}(x - 3)\).

Answer:

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