Question

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

Explanation:

Step1: Calculate 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 \((x_1, y_1)=(2, -8)\) and \((x_2, y_2)=(-6, 0)\). Then \(m=\frac{0 - (-8)}{-6 - 2}=\frac{8}{-8}=-1\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((-6, 0)\) (we could also use \((2, -8)\)). Substitute \(m = - 1\), \(x_1=-6\) and \(y_1 = 0\) into the point - slope form: \(y-0=-1(x - (-6))\), 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:

\(y=-x - 6\)