Question

write an equation of a line in point slope form given a slope of 3 and the point (9, -4).

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 \( (x_1,y_1)=(9,-4) \).

Step3: Substitute values into the formula

Substitute \( m = 3 \), \( x_1 = 9 \) and \( y_1=-4 \) into the point - slope formula \( y - y_1=m(x - x_1) \).
We get \( y-(-4)=3(x - 9) \), which simplifies to \( y + 4 = 3(x - 9) \).

Answer:

\( y + 4 = 3(x - 9) \)