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Is the function y=6–56x linear or nonlinear?

Question

Is the function y=6–56x linear or nonlinear?

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Solution

The function y=6–56x is a linear function. Here's why:

  1. A linear function has the form y = mx + b, where m and b are constants. m is the slope of the line, and b is the y-intercept.

  2. In the function y=6–56x, you can rearrange it to the form y = mx + b by rewriting it as y = -56x + 6.

  3. Here, m (the coefficient of x) is -56, and b (the constant term) is 6. Since the function can be written in the form y = mx + b, it is a linear function.

  4. Linear functions represent straight lines when graphed. The graph of y=6–56x would be a straight line with a slope of -56 and y-intercept of 6.

So, the function y=6–56x is linear.

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