Question

find the equation of the line written in point - slope form with the given slope and passes through the given point. use ( x ) as the independent variable.
slope ( = 3 )
point ( = (7, - 2) )

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 on the line.

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

We are given that the slope \(m = 3\) and the point \((x_1,y_1)=(7,- 2)\).

Step3: Substitute values into the formula

Substitute \(m = 3\), \(x_1=7\) and \(y_1=-2\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-2)=3(x - 7)\), which simplifies to \(y + 2=3(x - 7)\).

Answer:

\(y + 2=3(x - 7)\)