Line K passes through the point \( (15,18) \) and is parallel to the line given by \[ y=\frac{2}{3} x-6 \text {. } \] What is the equation of line K ? \( \quad \) Give your answer in the form \( y=m x+c \) where \( m \) and \( c \) are integers or fractions in their simplest forms.

To find the equation of line \( K \) that passes through the point \( (15, 18) \) and is parallel to the line \( y = \frac{2}{3}x - 6 \), follow these steps: 1. **Determine the Slope:** - The given line has a slope of \( \frac{2}{3} \). - Since parallel lines have the same slope, the slope \( m \) of line \( K \) is also \( \frac{2}{3} \). 2. **Use the Point-Slope Form:** - The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] - Plugging in the point \( (15, 18) \) and the slope \( m = \frac{2}{3} \): \[ y - 18 = \frac{2}{3}(x - 15) \] 3. **Simplify to Slope-Intercept Form:** - Distribute the slope on the right side: \[ y - 18 = \frac{2}{3}x - 10 \] - Add 18 to both sides to solve for \( y \): \[ y = \frac{2}{3}x + 8 \] So, the equation of line \( K \) is: \[ y = \frac{2}{3}x + 8 \] **Answer:** After simplifying, an equation for line K is \( y = \dfrac{2}{3}\,x\,+\,8 \).