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.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSA.CED.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).

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSA.CED.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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

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.HSF.LE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.1

CCSS.HSA.CED.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.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSA.CED.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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSA.CED.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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

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.

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSA.CED.A.2