Question

find an equation in point slope for the line that passes through the points (6, -2) and (-3, -4).

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(6, - 2)\) and \((x_2, y_2)=(-3, - 4)\). Then \( m=\frac{-4-(-2)}{-3 - 6}=\frac{-4 + 2}{-9}=\frac{-2}{-9}=\frac{2}{9} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((6, - 2)\) (we could also use \((-3, - 4)\)). Substitute \( m = \frac{2}{9} \), \( x_1 = 6 \) and \( y_1=-2 \) into the formula: \( y-(-2)=\frac{2}{9}(x - 6) \), which simplifies to \( y + 2=\frac{2}{9}(x - 6) \). If we use the point \((-3, - 4)\), substituting \( m=\frac{2}{9} \), \( x_1=-3 \) and \( y_1 = - 4 \) gives \( y-(-4)=\frac{2}{9}(x-(-3)) \), or \( y + 4=\frac{2}{9}(x + 3) \).

Answer:

Using the point \((6,-2)\): \( y + 2=\frac{2}{9}(x - 6) \) (or using the point \((-3,-4)\): \( y + 4=\frac{2}{9}(x + 3) \))