3. \( y=2 x-5 \)

Did you know that linear equations like \( y = 2x - 5 \) form the backbone of algebra and are key to understanding more complex mathematical concepts? This equation represents a straight line on a graph, where 2 is the slope (the steepness of the line) that indicates how much \( y \) changes for each unit increase in \( x \), and -5 is the y-intercept, which is the point where the line crosses the y-axis. In the real world, you can find linear equations in various scenarios, such as predicting costs, trends, or even determining distances. For instance, if you were tracking expenses and found that your spending increases by $2 for each additional item you buy (with a starting cost of $5), this equation captures that relationship. So, next time you're out shopping or budgeting, remember that linear equations help to make sense of our everyday financial decisions!