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State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.


y=2x-5

Short Answer

Expert verified

No, the equation y=2x-5 is not a linear equation.

Step by step solution

01

– Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as f(x)=mx+b, where m and b are real numbers.

02

– Given information.

The given equation is:

y=2x-5

Taking square on both sides.

y2=(2x5)2y2=2x5

03

– Check whether the equation is linear or not.

In the equation y2=2x-5the exponent of x is 1 and the exponent of y is 2.

The equation y2=2x-5is not a linear equation because y has an exponent other than 1.

The equation y2=2x-5is equivalent to y=2x-5. So, the equation y=2x-5is not linear.

Thus,the required answer is 鈥淣o鈥 because the equation y=2x-5is not a linear equation.

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