The point-slope equation you provided is actually slightly misformatted in your question. The correct point-slope form is usually written as y – y1 = m(x – x1), where m is the slope and (x1, y1) is a specific point on the line.
In your equation, y = 3x + 2, the slope m is 3, and the y-intercept (where the line crosses the y-axis) is 2. Therefore, we can interpret this equation directly as a linear function.
To express the linear function in the standard form of a linear equation, it can be rewritten as:
f(x) = 3x + 2
This means for any value of x, you can calculate f(x) to get the corresponding value of y on the line. For example, when x = 0, f(0) = 3(0) + 2 = 2. When x = 1, f(1) = 3(1) + 2 = 5.
Thus, the linear function represented by your point-slope equation is simply f(x) = 3x + 2.