Concept explainers
Suppose
when
To find : direct variation equation and its graph that relates x and y
Answer to Problem 22P
The direct variation equation that relations x and y is
Explanation of Solution
Given information :
Concept Involved:
Use the fact that if “ y varies directly with x ” then the equation relating x and y is
Substitute the given values of x and y in to the equation.
Solve the equation for k .
Back Substitute the k value in equation
To graph the equation, identify any two points satisfying the equation by picking some x values substituting in equation and finding the corresponding y value.
Calculation: Use the fact that if “ y varies directly with x ” then the equation relating x and y is
Substitute
Solve for k
Use the symmetric property of identity which states that if a=b, then b=a to rewrite the equation
To get k alone divide by -4 on both sides of the equation
Simplify fraction in left side and flip the bottom fraction and multiply with top in the right side of the equation
Multiply numerator with numerator and denominator with denominator in right side of the equation
Divide the numerator and denominator by common factor of the fraction
Simplify fraction in right side of the equation
Back Substitute the k value in equation
To graph the equation, identify any two points satisfying the equation by picking some x values substituting in equation and finding the corresponding y value.
| ||
Graph:
Conclusion:
The direct variation equation that relations x and y is
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