Question

write the standard form of an equation given the points (-1, \frac{1}{3}), (9, -3)

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-1,\frac{1}{3})\) and \((x_2, y_2)=(9, - 3)\). Then \(m=\frac{-3-\frac{1}{3}}{9 - (-1)}=\frac{-\frac{10}{3}}{10}=-\frac{1}{3}\).

Step2: Use point - slope form

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

Step3: Convert to standard form (\(Ax+By = C\))

Multiply through by 3 to eliminate fractions: \(3y - 1=-x - 1\). Then, add \(x\) to both sides and add 1 to both sides: \(x+3y=0\).

Answer:

The standard form of the equation is \(x + 3y=0\)