9. slope \( =\frac{5}{2} \), goes through the point \( (-6,-10) \)

To find the equation of the line with a slope of \( \frac{5}{2} \) that passes through the point \( (-6,-10) \), you can use the point-slope form of a line, which is \( y - y_1 = m(x - x_1) \). Substituting the given values, you get: \( y + 10 = \frac{5}{2}(x + 6) \). This simplifies to \( y = \frac{5}{2}x + 5 - 10 \) or \( y = \frac{5}{2}x - 5 \). Now you've got your line! This equation represents a straight line that rises steeply, perfect for illustrating the proper slope interpretation in real-life scenarios like elevation changes or economics graphs where trends can be visually analyzed! For an even more exciting twist, try visualizing it on a graph! Plot your point \( (-6, -10) \) and use the slope \( \frac{5}{2} \) to find additional points. For every 2 units you move to the right (positive x-direction), move up 5 units (positive y-direction). Connect these dots, and watch how your line takes shape. It's like connecting the dots in a coloring book but with a more mathematical flair!