Nebi has already typed 250 words. He then starts a timer and finds that he types 150 words in 3 minutes. If Nebi types at a constant rate, write a linear equation to represent the number of words w Nebi types m minutes after starting the timer.

To represent the number of words Nebi types, w, as a linear equation based on the time in minutes, m, we can use the concept of a constant rate.

First, let's analyze the given information. Nebi typed 250 words before starting the timer. After starting the timer, Nebi typed an additional 150 words in 3 minutes.

We can find Nebi's typing rate per minute by dividing the number of words typed in 3 minutes by the time in minutes:

Typing rate = Number of words / Time in minutes
Typing rate = 150 words / 3 minutes
Typing rate = 50 words per minute

Now that we know Nebi's typing rate is 50 words per minute, we can use this information to form the linear equation.

The equation for a straight line can be written in the form y = mx + b, where m represents the slope of the line, and b represents the y-intercept (the value of y when x = 0).

In this case, the number of words typed, w, is the dependent variable (y), and the time passed, m, is the independent variable (x). The slope (m) represents the typing rate, which is 50 words per minute.

So our equation becomes:

w = 50m + b

To determine the value of the y-intercept, b, we can substitute the values of w and m from the given information. Nebi already typed 250 words before starting the timer, which means when m = 0, w = 250.

Substituting these values into the equation, we have:

250 = 50(0) + b
250 = 0 + b
b = 250

Therefore, the linear equation representing the number of words Nebi types, w, as a function of time, m, is:

w = 50m + 250