Units for m & b in y=mx+b Equation

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In summary, the equation y = mx + b has units of kg x m/s^2 for both the slope, m, and the y-intercept, b. The units of m should be kg in order for mx to have the same units as y. However, the meaning of m and b in this equation can vary depending on the specific details and context of the situation.
  • #1
chelseaalyssa
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Homework Statement



In an equation of the format y=mx + b, where y=(m1-m2)g and x=acceleration (m/s2) ... what are the units for m and b?
(I know that m is the slope and b is the y-intercept, but what do they mean?)

Thanks :)
 
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  • #2
Welcome to PF :smile:

Each term, "mx" and "b", must have the same units as y.

So, first question: what are the units of y?

Next question, what units for m would result in mx having those same units?
 
  • #3
The units of y = kg x m/s^2

Therefore, the units of b must equal kg x m/s^2 as well.

In order for mx to have the same units as y, the units of m should be kg right?

Thanks for your help!
 
  • #4
Also - does kg x m/s^2 equal Newtons?
 
  • #5
Yes, to everything you said/asked in post #'s 3 & 4 :smile:

chelseaalyssa said:
(I know that m is the slope and b is the y-intercept, but what do they mean?)

That depends on the context, i.e. on the specific details of what x and y are and how they were measured or calculated.
 
  • #6
Ok great, Thanks!
 

FAQ: Units for m & b in y=mx+b Equation

1. What do the units for m and b represent in the equation y=mx+b?

The unit for m represents the slope of the line, which is the amount that y changes for every 1 unit of x. The unit for b represents the y-intercept, which is the point where the line crosses the y-axis.

2. Can the units for m and b be different?

Yes, the units for m and b can be different. The unit for m is typically a rate or a ratio, while the unit for b is typically the same as the unit for y.

3. Are the units for m and b the same in all linear equations?

No, the units for m and b can vary depending on the context of the problem. For example, in a distance-time graph, the unit for m would be in units of distance per unit of time, while the unit for b would be in units of distance.

4. How do the units for m and b affect the graph of a linear equation?

The unit for m affects the steepness of the line, while the unit for b affects the position of the line on the y-axis. Changing the units for m and b can result in a steeper or flatter line, and a higher or lower y-intercept.

5. Can the units for m and b be negative?

Yes, the units for m and b can be negative. A negative unit for m indicates a negative slope, which means the line is decreasing from left to right. A negative unit for b indicates that the line crosses the y-axis below the origin.

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