Question

write an equation of the line in point - slope form that passes through the given points. $(9,-\frac{2}{3})$ and $(7,\frac{4}{3})$ an equation of the line is (simplify your answer. type an equation. type your answer in point - slope form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(9,-\frac{2}{3})$ and $(x_2,y_2)=(7,\frac{4}{3})$. Then $m=\frac{\frac{4}{3}-(-\frac{2}{3})}{7 - 9}=\frac{\frac{4 + 2}{3}}{-2}=\frac{2}{-2}=-1$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(x_1,y_1)=(9,-\frac{2}{3})$ and $m=-1$, we get $y-(-\frac{2}{3})=-1(x - 9)$.

Answer:

$y+\frac{2}{3}=-1(x - 9)$