Question
If 6 ft long ribbon cost $30, 15 ft long costs $75, then the difference between the constant of proportionality and slope of the line 
= x + 1 is
- 10
- 15
- 30
Hint:
Constant of proportionality is the same as the slope of a straight line passing through the origin. Using the formula m=
we can find the value of slope or constant of proportionality. Here, we have to find the difference between the constant of proportionality and slope of the given linear equation using the given information in the question.
The correct answer is: 10
In the question it is given that, a 6 ft long ribbon cost $30 and 15 ft long costs $75.
We have to find the difference between the constant of proportionality and slope of the line = x + 1.
Here, x= length of ribbon and y= price of ribbon
So, x= 6 and 15 and y= 30 and 75.
Step 1: Find the constant of proportionality.
Constant of proportionality=m= . ..........................(1)
Put the value of x and y in eq. 1.
Step 2 : Find the slope of the line.
The given line is = x + 1.
Multiply both sides by 15.
On comparing the equation of line with y=mx+c we get,
m= 15 and c= 15.
Step 2: Find the difference between the constant of proportionality and the slope of the given linear equations.
Constant of proportionality= 5 and Slope= 15
Difference between the constant of proportionality and the slope= 15-5
= 10
Thus, the difference between the constant of proportionality and the slope of the given linear equations is 10.
Therefore, the correct option is a, i.e., 10.
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