Question

write an equation in point slope form given the points (3, 9) and (1, 6)

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Given points \( (3,9) \) and \( (1,6) \), let \( (x_1,y_1)=(3,9) \) and \( (x_2,y_2)=(1,6) \). Then \( m=\frac{6 - 9}{1 - 3}=\frac{-3}{-2}=\frac{3}{2} \).

Step2: Write the point - slope form

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \).

• Using the point \( (3,9) \) and \( m = \frac{3}{2} \), we substitute into the formula: \( y - 9=\frac{3}{2}(x - 3) \).
• Using the point \( (1,6) \) and \( m=\frac{3}{2} \), we substitute into the formula: \( y - 6=\frac{3}{2}(x - 1) \).

Answer:

\( y - 9=\frac{3}{2}(x - 3) \) or \( y - 6=\frac{3}{2}(x - 1) \)