Thinking With Math Models Unit Test

2.

Find the equation of the line that passes through the points (0, 5) and (1, 8)

Y=5x+3
Y=3x+5
Y=5x+0
Y=x+8

Correct Answer

A. Y=3x+5

Explanation

The equation of a line can be found using the formula y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (0, 5) and (1, 8). Substituting these values into the formula, we get (8 - 5) / (1 - 0) = 3/1 = 3. Therefore, the slope of the line is 3. Substituting the slope and the coordinates of one point (0, 5) into the equation y = mx + b, we can solve for b. 5 = 3(0) + b, which gives us b = 5. Therefore, the equation of the line is y = 3x + 5.

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3.

Find the equation of the line with a slope of -3 that passes through the point (2, -5)

Y=-3x+2
Y=2x-5
Y=-3x-5
Y=-3x+1

Correct Answer

A. Y=-3x+1

Explanation

Use the equation y=mx+b

Plug slope in for m

Use the x and y values from the coordinate point to plug into y=mx+b

Solve for b

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4.

Write an equation for the number of cups and the price per package:

Y=10/x
Y=x+2
Y=2.5x
Y=2.5x+5

Correct Answer

A. Y=10/x

Explanation

The equation y=10/x represents the relationship between the number of cups (y) and the price per package (x). This equation states that the value of y is equal to 10 divided by x. This means that as the price per package increases (x increases), the number of cups decreases (y decreases), and vice versa. The equation y=10/x accurately describes this inverse relationship between the number of cups and the price per package.

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5.

What type of relationship is modeled by the table?

Inverse
Direct
Linear

Correct Answer

A. Inverse

Explanation

It is inverse because the x value times the y value gives you the constant of 30 each time

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6.

What type of relationship is shown in the table above?

Inverse
Direct
Linear

Correct Answer

A. Direct

Explanation

The table shows a direct relationship between x and y. A direct relationship means that as the value of x increases, the value of y also increases proportionally. In this case, y is always 7 times the value of x. This consistent multiplicative relationship indicates a direct proportionality between the two variables.

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1

7.

What relationship represents the table above?

Inverse
Direct
Linear

Correct Answer

A. Linear

Explanation

The relationship represented by the given table is linear. This is because the values in the table show a consistent pattern of change, with a constant rate of increase or decrease. In a linear relationship, there is a direct correlation between the input and output values, and the graph of the relationship would be a straight line.

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8.

Write an equation to model the following situation: Jennie wants to rent a photo booth for her upcoming function. The photo booth charges $200 for coming to her location and an additional $100 per hour.

C=100/x
C=100h
C=200h+100
C=100h+200

Correct Answer

A. C=100h+200

Explanation

The equation c=100h+200 represents the situation where c is the total cost of renting the photo booth, h is the number of hours the booth is rented for, and 200 is the fixed cost for the booth to come to the location. The additional cost of $100 per hour is represented by 100h, as it is multiplied by the number of hours h. Adding the fixed cost of $200 to the additional cost gives the total cost of renting the photo booth.

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9.

Which of the following equations model the data above?

Y=30/x
Y=15x
Y=15x+15
Y=30/x

Correct Answer

A. Y=30/x

Explanation

The equation y=30/x models the data above because it represents a relationship where the value of y is inversely proportional to the value of x. As x increases, y decreases and vice versa. This is evident in the given data where as x increases, y decreases. The equation y=30/x captures this relationship accurately.

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10.

Which of the following equations model the data above?

Y=8/x
Y=1.5x
Y=2x+1
Y=5/2x-2

Correct Answer

A. Y=5/2x-2

Explanation

The equation y=5/2x-2 models the given data because it represents a linear relationship between x and y. The slope of the line is 5/2, which means that for every increase of 2 in x, y increases by 5. The y-intercept is -2, which means that when x is 0, y is -2. This equation accurately represents the pattern observed in the data.

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11.

Which of the following equations model the data above?

Y=7/x
Y=7x
Y=10/x
Y=7x+1

Correct Answer

A. Y=7x

Explanation

The equation y=7x models the given data because it represents a linear relationship between the variables x and y, where y is equal to 7 times x. This means that as x increases, y also increases at a constant rate. The equation y=7/x does not model the data because it represents a reciprocal relationship, where y decreases as x increases. The equation y=10/x does not model the data because it represents a reciprocal relationship with a different constant value. The equation y=7x+1 does not model the data because it includes an additional constant term of 1.

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Thinking With Math Models Unit Test

Find the equation of the line that passes through the points (1 , 3) and (2, 4)

Find the equation of the line that passes through the points (0, 5) and (1, 8)

Find the equation of the line with a slope of -3 that passes through the point (2, -5)

Write an equation for the number of cups and the price per package:

What type of relationship is modeled by the table?

What type of relationship is shown in the table above?

What relationship represents the table above?

Write an equation to model the following situation: Jennie wants to rent a photo booth for her upcoming function. The photo booth charges $200 for coming to her location and an additional $100 per hour.

Which of the following equations model the data above?

Which of the following equations model the data above?

Which of the following equations model the data above?