Linear Functions-points And Slopes

1.

Which graph is linear?

Top-Left

Top-Right

Bottom-Left

Bottom-Right

The graph that is linear is the one in the top-right position.

Explanation

The graph that is linear is the one in the top-right position.

2. Rate of change can also be referred to as the _______________ of a line.

The rate of change refers to how much a quantity changes in relation to another quantity. In the context of a line, the rate of change is commonly referred to as the slope. The slope represents the steepness or inclination of the line and indicates how much the dependent variable changes for a given change in the independent variable. Therefore, the correct answer for this question is slope.

Explanation

The rate of change refers to how much a quantity changes in relation to another quantity. In the context of a line, the rate of change is commonly referred to as the slope. The slope represents the steepness or inclination of the line and indicates how much the dependent variable changes for a given change in the independent variable. Therefore, the correct answer for this question is slope.

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3. Calculate the slope of the line that goes through
A(-4, 5) and B(2, -7)

2

-1/2

1/2

-2

None of the above

The slope of a line can be calculated using the formula (change in y)/(change in x). In this case, the change in y is -7 - 5 = -12 and the change in x is 2 - (-4) = 6. Therefore, the slope is -12/6 = -2.

Explanation

The slope of a line can be calculated using the formula (change in y)/(change in x). In this case, the change in y is -7 - 5 = -12 and the change in x is 2 - (-4) = 6. Therefore, the slope is -12/6 = -2.

4. Determine the slope of the line that passes through
(15,-8) and (10, 3)

11/5

1

-1

-11/5

To determine the slope of a line passing through two points, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is -8 - 3 = -11, and the change in x is 15 - 10 = 5. Therefore, the slope is -11/5.

Explanation

To determine the slope of a line passing through two points, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is -8 - 3 = -11, and the change in x is 15 - 10 = 5. Therefore, the slope is -11/5.

5. Identify the slope in the equation C = - 200 t + 540

C

200

T

540

None of the above

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Explanation

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6. If the first differences are _______________ then the relationship is linear.

If the first differences are constant, it means that the difference between consecutive terms in the sequence is always the same. This indicates a linear relationship, where each term can be obtained by adding a fixed value to the previous term. In a linear relationship, the rate of change between any two terms remains constant throughout the sequence.

Explanation

If the first differences are constant, it means that the difference between consecutive terms in the sequence is always the same. This indicates a linear relationship, where each term can be obtained by adding a fixed value to the previous term. In a linear relationship, the rate of change between any two terms remains constant throughout the sequence.

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7.

Determine the rate of change for the relation shown in the graph.

2

1/2

-1/2

-2

The rate of change for the relation shown in the graph is -1/2. This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1/2. In other words, as x increases, y decreases at a constant rate of 1/2.

Explanation

The rate of change for the relation shown in the graph is -1/2. This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1/2. In other words, as x increases, y decreases at a constant rate of 1/2.

8. Calculate the slope of the line that goes through (2, -1) and (0, -2)

2

-1/2

1/2

-2

None of the Above

To calculate the slope of a line, we use the formula: slope = (change in y) / (change in x). In this case, the change in y is -1 - (-2) = 1, and the change in x is 2 - 0 = 2. So, the slope is 1/2.

Explanation

To calculate the slope of a line, we use the formula: slope = (change in y) / (change in x). In this case, the change in y is -1 - (-2) = 1, and the change in x is 2 - 0 = 2. So, the slope is 1/2.

9.

Determine the rate of change for the relation shown in the table of values.

-2

-1/2

1/2

2

The rate of change for the relation shown in the table of values is -1/2. This means that for every unit increase in the input variable, the output variable decreases by 1/2.

Explanation

The rate of change for the relation shown in the table of values is -1/2. This means that for every unit increase in the input variable, the output variable decreases by 1/2.

10. Determine the slope of the line that passes through
(-9,7) and (2, -6)

-13/11

-11/13

11/13

13/11

To determine the slope of a line passing through two points, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is -6 - 7 = -13, and the change in x is 2 - (-9) = 11. Therefore, the slope is -13/11.

Explanation

To determine the slope of a line passing through two points, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is -6 - 7 = -13, and the change in x is 2 - (-9) = 11. Therefore, the slope is -13/11.

11. What is the slope of the relation y = -4/5x - 4

4

-4

4/5

-4/5

The slope of a linear relation is the coefficient of the x-term. In this case, the given equation is in the form y = mx + b, where m is the slope. Therefore, the slope of the relation y = -4/5x - 4 is -4/5.

Explanation

The slope of a linear relation is the coefficient of the x-term. In this case, the given equation is in the form y = mx + b, where m is the slope. Therefore, the slope of the relation y = -4/5x - 4 is -4/5.

12.

What is the slope from the bottom right of the hill to the top of the hill.

2.5

2/5

-2/5

-2.5

The slope from the bottom right of the hill to the top of the hill is -2.5. This means that for every unit of horizontal distance, there is a decrease of 2.5 units in vertical distance. In other words, the hill has a steep descent from the bottom right to the top.

Explanation

The slope from the bottom right of the hill to the top of the hill is -2.5. This means that for every unit of horizontal distance, there is a decrease of 2.5 units in vertical distance. In other words, the hill has a steep descent from the bottom right to the top.

13. Determine which ordered pairs are also in the relation where the rise is 3, the run is 2, and
(-4,10) lies on the line.

(-8, -4) and (0, 16)

(4, 22) and (-2,13)

(-4, -10) and (-16, 8)

(8, 22) and (-8, 4)

The given question states that the rise is 3 and the run is 2. This means that for every increase of 2 units in the x-coordinate, the y-coordinate increases by 3 units. We are also given that (-4, 10) lies on the line.

For the ordered pair (4, 22), the change in x-coordinate is 4 - (-4) = 8 units, and the change in y-coordinate is 22 - 10 = 12 units. The ratio of the change in y-coordinate to the change in x-coordinate is 12/8 = 3/2, which matches the given rise and run. Therefore, (4, 22) is in the relation.

For the ordered pair (-2, 13), the change in x-coordinate is -2 - (-4) = 2 units, and the change in y-coordinate is 13 - 10 = 3 units. The ratio of the change in y-coordinate to the change in x-coordinate is 3/2, which matches the given rise and run. Therefore, (-2, 13) is also in the relation.

Hence, the correct answer is (4, 22) and (-2, 13).

Explanation

The given question states that the rise is 3 and the run is 2. This means that for every increase of 2 units in the x-coordinate, the y-coordinate increases by 3 units. We are also given that (-4, 10) lies on the line.

For the ordered pair (4, 22), the change in x-coordinate is 4 - (-4) = 8 units, and the change in y-coordinate is 22 - 10 = 12 units. The ratio of the change in y-coordinate to the change in x-coordinate is 12/8 = 3/2, which matches the given rise and run. Therefore, (4, 22) is in the relation.

For the ordered pair (-2, 13), the change in x-coordinate is -2 - (-4) = 2 units, and the change in y-coordinate is 13 - 10 = 3 units. The ratio of the change in y-coordinate to the change in x-coordinate is 3/2, which matches the given rise and run. Therefore, (-2, 13) is also in the relation.

Hence, the correct answer is (4, 22) and (-2, 13).

14. Which ordered pairs are also in the relation where the rise is -2, the run is 3, and (6,2) lies on the line.

(-3, 4) and (3,8)

(-9, -12) and (-6, 2)

(0, 9) and (-2, 12)

(9, 0) and (12, -2)

The ordered pairs (9, 0) and (12, -2) are also in the relation because they satisfy the given conditions. The rise is -2, which means that the y-coordinate decreases by 2 units. The run is 3, which means that the x-coordinate increases by 3 units. Starting from the point (6, 2), if we decrease the y-coordinate by 2 units, we get (6, 0). If we increase the x-coordinate by 3 units, we get (9, 0). Similarly, starting from (6, 2), if we decrease the y-coordinate by 2 units, we get (6, 0). If we increase the x-coordinate by 3 units, we get (12, -2). Therefore, (9, 0) and (12, -2) are in the relation.

Explanation

The ordered pairs (9, 0) and (12, -2) are also in the relation because they satisfy the given conditions. The rise is -2, which means that the y-coordinate decreases by 2 units. The run is 3, which means that the x-coordinate increases by 3 units. Starting from the point (6, 2), if we decrease the y-coordinate by 2 units, we get (6, 0). If we increase the x-coordinate by 3 units, we get (9, 0). Similarly, starting from (6, 2), if we decrease the y-coordinate by 2 units, we get (6, 0). If we increase the x-coordinate by 3 units, we get (12, -2). Therefore, (9, 0) and (12, -2) are in the relation.

15. Calculate the rise length for the line going through A(3, 2) and B(-5, 0)

8

-8

-2

2

None of the above

The rise length is the vertical distance between two points on a line. To calculate it, we subtract the y-coordinate of point A from the y-coordinate of point B. In this case, the y-coordinate of A is 2 and the y-coordinate of B is 0. Therefore, the rise length is 2.

Explanation

The rise length is the vertical distance between two points on a line. To calculate it, we subtract the y-coordinate of point A from the y-coordinate of point B. In this case, the y-coordinate of A is 2 and the y-coordinate of B is 0. Therefore, the rise length is 2.