Question

find the point-slope equation for the line that passes through the points (5, 18) and (-4, -18). use the first point in your equation.

y - ? = (x - )

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, \((x_1, y_1)=(5, 18)\) and \((x_2, y_2)=(-4, -18)\). So, \(m=\frac{-18 - 18}{-4 - 5}=\frac{-36}{-9}=4\).

Step2: Identify the point and slope for point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. We use the first point \((5, 18)\), so \(y_1 = 18\), \(x_1 = 5\) and \(m = 4\).

Answer:

\(y - 18 = 4(x - 5)\)