Rate of change in math

Question

2y = 7x + 6

Find the rate of change please

Answer 1

Hello, thank you for taking the time to post your question!

The “rate of change” means finding the slope, so I would put the equation into the form y = mx + b and then see what the value of “m” is

2y = 7x + 6

y = 7/2x + 3

so the rate of change here is 7/2 or 3.5

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Travis,

The rate of change in this equation is the same as the slope of a line.

There are a few steps to follow when finding the rate of change/slope:

1. The equation must be written in slope intercept form: y = mx + b. Where ‘m’ = the rate of change/slope and ‘b’ = the initial value/y-intercept.
2. The equation 2y = 7x + 6 is not in slope intercept form since there is a ‘2’ in front of the ‘y’. For it to be in the correct form, the ‘y’ must be by itself.
3. We must isolate the ‘y’ by dividing ‘2’ from everything on both sides of the equation.
4. (2/2)y = (7/2)x + (6/2)
5. Simplify and rewrite your equation in slope intercept form to determine the rate of change/slope:
6. y = 7/2x + 3 (Improper Fraction)
7. OR
8. y = 3 1/2x + 3 (Mixed Number)
9. OR
10. y = 3.5x + 3 (Decimal)
11. Choose ONE form to write the rate of change/slope in this equation
12. Check if one way is asked/expected in problem or by teacher before using the easiest one.
13. The final answer should be written (ONE WAY exactly same as you did for ‘m’ in final equation):
14. The rate of change is 7/2.
15. OR
16. The rate of change is 3 1/2.
17. OR
18. The rate of change is 3.5.

Answer 3

Hello Travis,

the rate of change here will be the slope of the line. To find it, divide both sides by 2 to isolate the y:

y = (7/2)x + 6/2 = (7/2)x + 3

The slope of the line is 7/2, and that is also the rate of change👍