Question

what is an equation of the line that passes through the points (-8, 3) and (-2, 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, \((x_1, y_1)=(-8, 3)\) and \((x_2, y_2)=(-2, 0)\). So, \( m=\frac{0 - 3}{-2 - (-8)}=\frac{-3}{6}=-\frac{1}{2} \).

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 \((-2, 0)\). Substitute \( m = -\frac{1}{2} \), \( x_1=-2 \) and \( y_1 = 0 \) into the formula: \( y-0=-\frac{1}{2}(x + 2) \).

Step3: Simplify the equation

Simplify \( y=-\frac{1}{2}x-1 \). We can also write it in standard form \( x + 2y=-2 \) or in slope - intercept form \( y=-\frac{1}{2}x - 1 \).

Answer:

The equation of the line is \( y = -\frac{1}{2}x-1 \) (or \( x + 2y=-2 \))