Question

write the standard form of an equation given two points (-1, 1/3), (4, -3)

Explanation:

Step1: Identify the two points

Let the two points be \( P(-1, \frac{1}{3}) \) and \( Q(4, -3) \).

Step2: Calculate the slope (\(m\))

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the values: \( m = \frac{-3 - \frac{1}{3}}{4 - (-1)} = \frac{-\frac{10}{3}}{5} = -\frac{2}{3} \).

Step3: Use point - slope form

The point - slope form is \( y - y_1 = m(x - x_1) \). Let's use point \( P(-1, \frac{1}{3}) \).
\( y - \frac{1}{3} = -\frac{2}{3}(x + 1) \).

Step4: Convert to standard form (\(Ax + By = C\))

Multiply through by 3 to eliminate fractions: \( 3y - 1 = -2(x + 1) \).
Expand the right - hand side: \( 3y - 1 = -2x - 2 \).
Rearrange the terms: \( 2x + 3y = -1 \).

Answer:

The standard form of the equation of the line passing through the points \((-1,\frac{1}{3})\) and \((4, - 3)\) is \(2x+3y=-1\)