6. \( y=-8 x+16 \) 8. \( y=-\frac{3}{4} x+5 \) 7. 7. 10. \( y=x^{2}-4=-\frac{5}{8} x+10 \) 12. \( y=\sqrt{x+5}, y \geq 0 \) 11. \( y=(x-6)^{2} \) 13. \( y=\sqrt{x}-7, y \geq-7 \)

Let’s take a glimpse into the fascinating world of linear equations! The equation \( y=-8x+16 \) represents a straight line with a steep slope of -8, indicating that as x increases, y decreases rapidly. This can be visualized as a downward slanting line, starting high at \( y=16 \) when \( x=0 \). Such equations are prevalent in real life; for instance, calculating profit margins or predicting costs in various businesses often relies on linear relationships. Now, shifting gears to quadratic equations, \( y=x^{2}-4 \) reveals a classic parabolic shape that opens upwards. The intersection points with other equations, like \( -\frac{5}{8}x+10 \), can lead to intriguing solutions and insights about a situation's changing dynamics. Quadratics can model scenarios like projectile motion, where the height of an object varies with time, making them a staple in physics as well as in everyday problem-solving!