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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-2, 0)\) and \((x_2, y_2)=(4, -9)\). Then \(m=\frac{-9 - 0}{4 - (-2)}=\frac{-9}{6}=-\frac{3}{2}\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((-2, 0)\) and \(m =-\frac{3}{2}\). Substitute these values into the formula: \(y - 0=-\frac{3}{2}(x - (-2))\), which simplifies to \(y=-\frac{3}{2}(x + 2)\).
Expand the right - hand side: \(y=-\frac{3}{2}x-3\).

(For graphing: Plot the points \((-2, 0)\) and \((4, -9)\) on the coordinate plane. Then draw a straight line passing through these two points.)

Answer:

The equation of the line is \(y =-\frac{3}{2}x - 3\). To graph the line, plot the points \((-2,0)\) and \((4, - 9)\) and draw a straight line through them.