Question

a point on a line and its slope are given. find the point - slope form of the equation of the line.
p=(5,2), m = -\frac{3}{4}
the point - slope form of the equation of the line is
(use integers or fractions for any numbers in the equation.)

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

We are given the point \(P=(5,2)\), so \(x_1 = 5\) and \(y_1=2\). The slope \(m=-\frac{3}{4}\).

Step3: Substitute values into the formula

Substitute \(x_1 = 5\), \(y_1 = 2\) and \(m=-\frac{3}{4}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 2=-\frac{3}{4}(x - 5)\).

Answer:

\(y - 2=-\frac{3}{4}(x - 5)\)