Write an equation in slope-intercept form for the line with slope 4 and \( y \)-intercept 1 . Then graph the line.

The equation of a line in slope-intercept form is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Given a slope of 4 and a \( y \)-intercept of 1, the equation becomes \( y = 4x + 1 \). To graph this line, start at the \( y \)-intercept (0,1) on the \( y \)-axis. From there, use the slope: rise 4 units up and run 1 unit to the right to find another point on the line at (1,5). Now, you can draw a straight line through the points (0,1) and (1,5), extending in both directions. If you want to remember this method, think of slope as a “rise over run” journey, where each step up or over brings you to the next dot on your graph! Keeping track can make graphing feel like a fun puzzle. Understanding how a linear equation represents a relationship can help in various real-world scenarios such as budgeting or calculating distance over time. For instance, if you saw this equation in a business context, it could represent the cost of goods based on units sold, where the slope indicates the cost per unit and the intercept indicates fixed costs, providing you a clear picture of expenses!