Question

questions
what is an equation of the line that passes through the points (2, -8) and (-6, 0)?

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, \((x_1,y_1)=(2,-8)\) and \((x_2,y_2)=(-6,0)\). So, \( m=\frac{0 - (-8)}{-6 - 2}=\frac{8}{-8}=-1 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-6,0)\) (we could also use \((2,-8)\)). Substitute \( m=-1 \), \( x_1=-6 \), and \( y_1 = 0 \) into the formula: \( y-0=-1(x - (-6)) \), which simplifies to \( y=-x - 6 \). We can also check with the other point: substitute \( x = 2 \) into \( y=-x - 6 \), we get \( y=-2 - 6=-8 \), which matches the point \((2,-8)\).

Answer:

The equation of the line is \( y=-x - 6 \) (or other equivalent forms like \( x + y=-6 \))