Question

write the equation of the line that passes through the points (-6, -9) and (-8, -1). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1=-6,y_1 = - 9,x_2=-8,y_2=-1 \). So \( m=\frac{-1-(-9)}{-8 - (-6)}=\frac{-1 + 9}{-8 + 6}=\frac{8}{-2}=-4 \).

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 \((-6,-9)\) (we could also use \((-8,-1)\)). Substitute \( m=-4,x_1=-6,y_1=-9 \) into the formula: \( y-(-9)=-4(x - (-6)) \), which simplifies to \( y + 9=-4(x + 6) \).

Answer:

\( y + 9=-4(x + 6) \)