Final answer:
To write equations in the form y = mx + b, identify the slope (m) as the change in y over the change in x, and the y-intercept (b) as the y value when x=0. Equations y = x + 4 and y = 100x + 2,000 were provided as examples.
Step-by-step explanation:
To write an equation in the form of y = mx + b, we need to identify the slope (m) and the y-intercept (b). The slope represents the change in y for each unit of change in x (rise over run), while the y-intercept is the value of y when x is zero, indicating where the line crosses the y-axis.
For instance, if we have a situation where the total number of hours required for a project (y) depends on the square footage of the project area (x), measured in units of 1,000, with each 1,000 square feet taking an hour plus an additional 4 hours of setup time, the equation would be: y = x + 4.
Another example could be calculating the total payment (y) based on the number of students (x) in a class. If each student is charged $100, and there is a fixed cost of $2,000, the equation would be: y = 100x + 2,000.