Transforming Linear Functions Quiz! Test

1.

The slope is steeper before the slip.

The slope is unchanged.

Cannot be determined.

There is no slope involved.

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Explanation

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2. Given a linear function with a slope of -4/3, how will the graph differ if the slope changed to 4/3?

The steepness of the line increases.

The slope of the line changes from increasing to decreasing.

The slope of the line changes from decreasing to increasing.

There is no change in the graph of the line.

The given linear function has a slope of -4/3, which means that the line is decreasing as it moves from left to right. If the slope changes to 4/3, the line will change from decreasing to increasing as it moves from left to right. This means that the steepness of the line will increase, as it will become steeper in the positive direction. Therefore, the correct answer is "The slope of the line changes from decreasing to increasing."

Explanation

The given linear function has a slope of -4/3, which means that the line is decreasing as it moves from left to right. If the slope changes to 4/3, the line will change from decreasing to increasing as it moves from left to right. This means that the steepness of the line will increase, as it will become steeper in the positive direction. Therefore, the correct answer is "The slope of the line changes from decreasing to increasing."

3.

Y = 2/3x - 6

Y = -2/3x - 1

Y = -2/3x + 4

Y = 2/3x + 4

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Explanation

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4.

The amount he charges for each job will increase by $10.

The amount he charges for each job will decrease by $10.

The amount he charges per hour will increase by $10.

The amount he charges per hour will decrease by $10.

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Explanation

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5.

Y = 0.25x + 40.25

Y = 0.15x + 40.25

Y = 0.15x + 29.75

Y = 0.25x + 29.75

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Explanation

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6.

The slope of the Rider truck is steeper.

The slope of the I-Haul truck is steeper.

The slope of the Budjet truck is steeper.

Cannot be determined

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Explanation

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7. The line y= 2/5x + 4 is transformed to y = 4/5x + 4. How does this new rotation affect the graph?

The slope decreases; therefore, the line is closer to the y-axis and the steepness increases

The slope decreases; therefore, the line is closer to the x-axis and the steepness decreases

The slope increases; therefore, the line is closer to the x-axis and the steepness decreases

The slope increases; therefore, the line is closer to the y-axis and the steepness increases

When the slope of a line increases, it becomes steeper. In this case, the slope changes from 2/5 to 4/5, which means it increases. As a result, the line becomes closer to the y-axis and its steepness increases.

Explanation

When the slope of a line increases, it becomes steeper. In this case, the slope changes from 2/5 to 4/5, which means it increases. As a result, the line becomes closer to the y-axis and its steepness increases.

8.

The slope would increase.

The y-intercept would increase.

The slope and y-intercept would decrease.

The slope and y-intercept would stay the same.

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Explanation

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9. Determine the slope of the line 6x + 3y = 6. As the x-value increases, how would you describe movement along the line?

1 unit to the right, 2 units down

1 unit to the left, 2 units down

2 units to the left, 1 unit down

2 units to the right, 1 unit up

The given equation can be rewritten in the slope-intercept form as y = -2x + 2. This means that for every 1 unit increase in the x-value, the y-value decreases by 2 units. Therefore, as the x-value increases, movement along the line can be described as 1 unit to the right and 2 units down.

Explanation

The given equation can be rewritten in the slope-intercept form as y = -2x + 2. This means that for every 1 unit increase in the x-value, the y-value decreases by 2 units. Therefore, as the x-value increases, movement along the line can be described as 1 unit to the right and 2 units down.

10.

The pool company is charging more per hour.

The pool company started with a lower service call fee.

It will take less time for a customer's bill to reach $90.

After 6 hours a customer will be billed more than $100.

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Explanation

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11. The function f(x) = -2/3x + 2 can be formed by shifting the function y = -2/3x in which way?

Vertical shift up 2

Reflection over the x-axis

Vertical shift down 2

Horizontal shift to the left 2

The function f(x) = -2/3x + 2 can be formed by shifting the function y = -2/3x vertically up by 2 units. This is because the constant term +2 in the function f(x) causes the graph to shift upwards by 2 units compared to the original function y = -2/3x.

Explanation

The function f(x) = -2/3x + 2 can be formed by shifting the function y = -2/3x vertically up by 2 units. This is because the constant term +2 in the function f(x) causes the graph to shift upwards by 2 units compared to the original function y = -2/3x.