Question

graph the line that passes through the points (-2, 0) and (4, -9) and determine the equation of the line.

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(-2, 0)\) and \((x_2, y_2)=(4, -9)\). So, \(m=\frac{-9 - 0}{4 - (-2)}=\frac{-9}{6}=-\frac{3}{2}\).

Step2: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((-2, 0)\) and \(m = -\frac{3}{2}\), we get \(y - 0=-\frac{3}{2}(x - (-2))\), which simplifies to \(y=-\frac{3}{2}(x + 2)\). Expanding this, \(y=-\frac{3}{2}x-3\).

Answer:

The equation of the line is \(y = -\frac{3}{2}x-3\)