Question

use the point - slope form to write the equation of a line that passes through the point (5, 10) with a slope of $-\frac{11}{10}$.

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 that the point \((x_1,y_1)=(5,10)\) and the slope \(m =-\frac{11}{10}\).

Step3: Substitute values into the formula

Substitute \(x_1 = 5\), \(y_1=10\) and \(m=-\frac{11}{10}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 10=-\frac{11}{10}(x - 5)\).

Answer:

\(y - 10=-\frac{11}{10}(x - 5)\)