Question

graph the line that passes through the points (6, 4) and (3, 0) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For the points \((6, 4)\) and \((3, 0)\), we have \( x_1 = 6 \), \( y_1 = 4 \), \( x_2 = 3 \), \( y_2 = 0 \). So, \( m = \frac{0 - 4}{3 - 6} = \frac{-4}{-3} = \frac{4}{3} \).

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 \((3, 0)\). Substituting \( m=\frac{4}{3} \), \( x_1 = 3 \), and \( y_1 = 0 \) into the point - slope form, we get \( y - 0=\frac{4}{3}(x - 3) \).

Step3: Simplify the equation

Simplify \( y=\frac{4}{3}(x - 3) \). Distribute the \(\frac{4}{3}\) on the right - hand side: \( y=\frac{4}{3}x-4 \).

Answer:

The equation of the line is \( y = \frac{4}{3}x - 4 \)