Find the equation of the given line. Slope is \( \frac{2}{3} ;(6,3) \) on line

To find the equation of the line, we can use the point-slope form of the equation \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_1, y_1)\) is a point on the line. Given the slope \( m = \frac{2}{3} \) and the point \((6, 3)\): \[ y - 3 = \frac{2}{3}(x - 6) \] Now, let's simplify that: \[ y - 3 = \frac{2}{3}x - 4 \] \[ y = \frac{2}{3}x - 1 \] So, the equation of the line is \( y = \frac{2}{3}x - 1 \). If you have ever wondered how slopes work in the real world, think of them as the steepness of a hill. A slope of \( \frac{2}{3} \) means that for every 3 units you move horizontally, you move up 2 units vertically. This is like walking up a gentle hill, where the incline is not too steep, making it manageable to climb! When using point-slope form, a common mistake is forgetting to include the point coordinates in the equation. Be careful to substitute the correct \( x_1 \) and \( y_1 \) values from your point, as it ensures that your line passes through the specified point, maintaining accuracy in your calculations.