40. A line has the equation \( 3 x-5 y=15 \). What is its slope?

To find the slope of the line given by the equation \(3x - 5y = 15\), we can rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope. First, isolate \(y\): 1. Subtract \(3x\) from both sides: \(-5y = -3x + 15\) 2. Divide everything by \(-5\): \(y = \frac{3}{5}x - 3\) Now we can see that the slope \(m\) is \(\frac{3}{5}\). A line's slope indicates how steep it is and the direction it goes. A slope of \(\frac{3}{5}\) means that for every 5 units you move to the right (positive x-direction), the line rises 3 units (positive y-direction). It's like a fun hike—up a gentle incline where you can take in the sights without getting too breathless! Understanding slopes is not just a mathematical concept; it’s everywhere in real life! For example, road gradients are determined by slope. If you're driving up a hill with a slope, it helps you understand how steep the road is, which can impact how fast you drive. So next time you're on a bike ride or hiking, think about those slopes!