`(2)/(3)x+3y=2`
If the slope of the equation shown above is 6. What is the value of c?

Options

A. `-4`
B. `-(1)/(9)`
C. `(1)/(3)`
D. `4`

Answer

B

Explanation

Difficult: Medium
Category: Heart of Algebra/ Linear Equations
Strategic Advice: Don't overthink a question like this. It is asking about slope and you have an equation, so write the equation in slope-intercept form and see where that takes you.
Getting to the Answer: When an equation is written in slope-intercept form `(y=mx+b)`, m is the slope of the line. Rewritte the given equations in this form by subtracting `(2)/(3)x` from both sides and then dividing both sides by c:
`(2)/(3)x+cy=2`
`cy=(-2)/(3)x+2`
`y=((-2)/(3)x)/(c)+(2)/(c)`
Now, set the coefficient of x equal to the given slope (6) and solve for c. The coefficient is a fraction
`(6)/(1)=((-2)/(3))/(c)`
`6c=(-2)/(3)`
`c=(-2)/(3)+6`
`c=(-2)/(3)times(1)/(6)=(-1)/(9)`
The value of c is `(-1)/(9)`, which is (B).