Assume y = mx + b If the units for x is units of meters and the units for y units of seconds, then what must the units for (m) and (b) be?
look at the units:
s = s/m * m + s
I don't understand how you got b? can you explain?
y = mx + b
s = (s/m) * m +b
s = s + b (m cancel out)
s - s = b ?
How did you get ?
s = s/m * m + s
these are units, not variables.
Units on the left must be the same as units on the right.
To determine the units of (m) and (b), we need to consider the equation y = mx + b.
Given that the units for x are meters and the units for y are seconds, we can determine the units for (m) and (b) by observing how the units of the equation balance.
In the equation, the product of (m) and x must have the same units as y for the equation to make sense. Therefore, the units of (m * x) should be seconds.
Since the units for x are meters, we need to find a conversion factor to convert meters to seconds. This conversion factor will have units of seconds/meter.
Let's call this conversion factor k (k = seconds/meter). Therefore, (m * x) can be written as (m * x * k) to have the same units as y.
Now, (m * x * k) has units of seconds, and y also has units of seconds. This means that the product of (m * x * k) should equal the units of y, which is seconds.
Therefore, (m * x * k) = seconds. By dividing both sides of the equation by (x * k), we can solve for (m):
m = seconds / (x * k)
Simplifying further, we have:
m = seconds / (meters * (seconds/meter))
The seconds unit in the numerator cancels out with the seconds unit in the denominator:
m = 1 / meters
So, the units for (m) are 1/meter or "per meter."
Now, let's consider the units for (b). The equation y = mx + b tells us that (b) is the y-intercept, which represents a value, not a rate or ratio.
Since y has units of seconds, (b) must also have units of seconds to maintain consistency in the equation.
Thus, the units for (b) are seconds.
In conclusion, the units for (m) are 1/meter or "per meter," and the units for (b) are seconds.