write an equation in point - slope form for the line that passes through the given points. (3, 3), (6, 7)

Explanation:

Step1: Calculate the slope

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Given ((x_1,y_1)=(3,3)) and ((x_2,y_2)=(6,7)), then (m=\frac{7 - 3}{6 - 3}=\frac{4}{3}).

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)). Using the point ((3,3)) and (m = \frac{4}{3}), we get (y - 3=\frac{4}{3}(x - 3)). (We could also use the point ((6,7)): (y - 7=\frac{4}{3}(x - 6)))

Answer:

(y - 3=\frac{4}{3}(x - 3)) or (y - 7=\frac{4}{3}(x - 6))