Linear or Exponential?

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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed. It has the form y = mx + b, where m is the slope and b is the y-intercept.

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What is an exponential equation?

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An exponential equation is an equation in which a variable appears in the exponent. It has the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

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How can you identify a linear relationship in a table of values?

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A linear relationship in a table of values shows a constant rate of change, meaning the difference between consecutive y-values is the same for equal intervals of x.

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How can you identify an exponential relationship in a table of values?

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An exponential relationship in a table of values shows a constant multiplicative rate of change, meaning each y-value is a constant multiple of the previous y-value.

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What is the slope in a linear equation?

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The slope (m) in a linear equation represents the rate of change of y with respect to x. It indicates how steep the line is.

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What does the y-intercept represent in a linear equation?

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The y-intercept (b) in a linear equation is the point where the line crosses the y-axis, representing the value of y when x is 0.

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What is the general form of an exponential function?

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The general form of an exponential function is y = ab^x, where a is the initial value, b is the growth (if b > 1) or decay (if 0 < b < 1) factor, and x is the exponent.

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What is the difference between linear growth and exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

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What is a common example of a linear function in real life?

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A common example of a linear function is calculating the total cost of items at a fixed price, such as y = 5x, where x is the number of items and y is the total cost.

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What is a common example of an exponential function in real life?

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A common example of an exponential function is population growth, where the population increases by a percentage each year, such as y = 100(1.05)^x.