Question

there is a line that includes the point (4, -5) and has a slope of \\(\frac{1}{8}\\). 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 line 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 values of \(x_1\), \(y_1\) and \(m\)

We are given the point \((4,-5)\), so \(x_1 = 4\) and \(y_1=-5\). The slope \(m=\frac{1}{8}\).

Step3: Substitute values into the formula

Substitute \(x_1 = 4\), \(y_1=-5\) and \(m = \frac{1}{8}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-5)=\frac{1}{8}(x - 4)\), which simplifies to \(y + 5=\frac{1}{8}(x - 4)\).

Answer:

\(y + 5=\frac{1}{8}(x - 4)\)