If you want the calculator to graph ##y = \frac{2x}{3x}##, write it as y = (2x)/(3x)Beanyboy said:Summary: Functions of both graphs are identical on calculator.
On my graphing calculator y = 2x/3x gives precisely the same graph as y = 2/3x squared. How is this possible?
Thanks. Much appreciated.willem2 said:Multiplications and divisions should be evaluated from left to right. 2x/3x = (2x/3) x = (2/3) x^2
The equation 2x/3x can be simplified to 2/3, which is then multiplied by x squared to get 2/3x squared. This is known as the power rule in algebra, where the coefficient (2/3) is multiplied by the variable (x) raised to the power (2).
The variable is squared in the equation because it follows the power rule in algebra. When dividing two terms with the same variable, the exponents are subtracted from each other. In this case, x divided by x results in an exponent of 1, which is then subtracted from the original exponent of 3, resulting in x squared.
No, the equation is already in its simplest form. The only way to simplify it further would be to factor out the common factor of 2/3, but this would not change the overall value of the equation.
To solve the equation, you can multiply both sides by 3x, which will cancel out the denominators and leave you with 2x = 2x squared. Then, you can subtract 2x from both sides to get 0 = 2x squared - 2x. Finally, you can factor out x and solve for its values using the quadratic formula.
The difference between the two is that 2x/3x is a fraction with the variable x in the numerator and denominator, while 2/3x squared is a fraction with the variable x squared in the denominator. This difference is due to the power rule in algebra, where the exponents are subtracted when dividing two terms with the same variable.