7. What is the gradient of the line \( 3 y-2 x=6 \) ? \( \begin{array}{llll}\text { (a) }-\frac{3}{2} & \text { (b) }-\frac{2}{3} & \text { (c) } \frac{2}{3} & \text { (d) } \frac{3}{2}\end{array} \)

To find the gradient of the line represented by the equation \( 3y - 2x = 6 \), we need to rearrange it into slope-intercept form \( y = mx + b \) where \( m \) is the gradient. Start by isolating \( y \): 1. Add \( 2x \) to both sides: \( 3y = 2x + 6 \) 2. Divide everything by 3: \( y = \frac{2}{3}x + 2 \) Now, the gradient \( m \) is \( \frac{2}{3} \). So, the answer is \( (c) \frac{2}{3} \). For a touch of fun, think of gradients as the express elevators of a building; the steeper the gradient, the faster you go up or down! If you're looking for common calculations with gradients, many people forget to check their signs or misinterpret the slope's rise over run concept. Always visualize your graph; it helps catch those pesky errors!