Linear and Exponential Equations

Answer explanation

The equation of a line in point-slope form is y - y1 = m(x - x1). Here, m = -2/3 and the point is (3, 2). Substituting these values gives y - 2 = -2/3(x - 3), which simplifies to y = 2 - (2/3)(x - 3).

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Answer explanation

To find the equation, use the point-slope form: y - y1 = m(x - x1). Here, m = 4 and the point is (-5, 10). Plugging in gives y - 10 = 4(x + 5), which simplifies to y = 10 + 4(x + 5). Thus, the correct choice is y=10+4(x+5).

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

The starting point is (1, 5) and the output values are multiplied by 3 each time.

Answer explanation

The function starts at (1, 5) and multiplies by 3 each time, indicating an exponential growth. The correct model is y=5(3)^(x-1), where 5 is the initial value and 3 is the growth factor.

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

The starting point is (3, 400) and the output values are divided by 2 each time.

Answer explanation

The function starts at (3, 400) and halves the output each time, indicating an exponential decay. The correct model is y=400(1/2)^(x-3), which reflects the starting point and the halving behavior.

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

A line goes through the points (-3, 2) and a slope of 3.

Answer explanation

To find the equation of the line, use the point-slope form: y - y1 = m(x - x1). Here, m = 3 and the point (-3, 2) gives y - 2 = 3(x + 3). Rearranging leads to y = 2 + 3(x + 3), which matches the correct choice.

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.LE.A.1

Write the equation of the linear or exponential function that best models the given information:

A line goes through the points (5, -10) and (-3, 2).

Answer explanation

To find the equation of the line through (5, -10) and (-3, 2), we calculate the slope as m = (2 - (-10)) / (-3 - 5) = 3/2. Using point-slope form, we get y + 10 = -3/2(x - 5), simplifying to y = -10 - (3/2)(x - 5).

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

Answer explanation

The correct choice is y=5+\frac{7}{2}(x+3) because it represents a linear function with a slope of \frac{7}{2} and a y-intercept adjusted by 5, fitting the given data points accurately.

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

Answer explanation

The correct choice is y=81(1/3)^x, indicating an exponential decay. This function starts at 81 and decreases by a factor of 1/3 for each unit increase in x, fitting the given information about the model.

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CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

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CCSS.HSF.LE.B.5

Write the equation of the linear or exponential function that best models the given information:

Answer explanation

The correct choice is y=2(2)^x, which represents an exponential function. It indicates that the value of y doubles as x increases by 1, fitting the pattern of exponential growth described in the problem.

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CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write the equation of the linear or exponential function that best models the given information:

Answer explanation

The correct equation is y=5-\frac{5}{3}(x+1) because it represents a linear function with a negative slope, indicating a decrease as x increases, which fits the given information.

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CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2