# Algebra 1 - 6.1 Homework (Rates Of Change)

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
P
Community Contributor
Quizzes Created: 3 | Total Attempts: 348
Questions: 19 | Attempts: 122

Settings

Determining rates of change from graphs and tables; determine slope.

• 1.

### Find the rate of change: People Cost (dollars) 2 7.90 3 11.85 4 15.80 5 19.75 6 23.70

Explanation
The rate of change in this scenario is \$3.95 per person. This means that for every additional person, the cost increases by \$3.95. The answer is given as \$3.95, \$3.95, which suggests that the rate of change is consistent and applies to both the number of people and the cost.

Rate this question:

• 2.

### Find the rate of change:

Explanation
The rate of change is 2/3 or two-thirds. This means that for every unit increase in the independent variable, there is a corresponding increase of 2/3 in the dependent variable.

Rate this question:

• 3.

### Find the rate of change:

Explanation
The rate of change is 4. This means that for every unit increase in the independent variable, there is a corresponding increase of 4 in the dependent variable.

Rate this question:

• 4.

### Find the slope of the line:

Explanation
The given answer, -3/1, represents the slope of the line. The slope is a measure of how steep a line is and is determined by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In this case, the slope is -3/1, which means that for every 1 unit increase in the horizontal direction, the line decreases by 3 units in the vertical direction. This indicates a steep downward slope. The -3 value alone represents the y-intercept, which is the point where the line crosses the y-axis.

Rate this question:

• 5.

### Find the slope of the line that passes thru each pair of points: (3, 2) and (5, 6)

Explanation
The slope of a line passing through two points can be found using the formula: (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (3, 2) and (5, 6). Plugging these values into the formula, we get (6 - 2) / (5 - 3) = 4/2 = 2. Therefore, the slope of the line passing through these two points is 2.

Rate this question:

• 6.

### Find the slope of the line that passes thru each pair of points: (4, 8) and (8, 11)

Explanation
The slope of a line passing through two points can be found using the formula: slope = (change in y)/(change in x). In this case, the change in y is 11 - 8 = 3, and the change in x is 8 - 4 = 4. Therefore, the slope is 3/4.

Rate this question:

• 7.

### Find the slope of the line that passes thru each pair of points: (-2, 1) and (1, -2)

Explanation
The slope of a line passing through two points can be found using the formula: slope = (change in y-coordinates)/(change in x-coordinates). In this case, the change in y-coordinates is (-2 - 1) = -3 and the change in x-coordinates is (1 - (-2)) = 3. Therefore, the slope is -3/3, which simplifies to -1.

Rate this question:

• 8.

### Find the slope of the line that passes thru each pair of points: (-8, 0) and (1, 5)

Explanation
The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the points are (-8, 0) and (1, 5). Plugging the values into the formula, we get (5 - 0) / (1 - (-8)) which simplifies to 5/9. Therefore, the slope of the line passing through these two points is 5/9. The second option, -5/-9, is the same as 5/9 when simplified.

Rate this question:

• 9.

### Find the slope of the line that passes thru each pair of points: (-4, -5) and (-9, -1)

Explanation
To find the slope of a line passing through two points, we use the formula (y2 - y1) / (x2 - x1). In this case, the points are (-4, -5) and (-9, -1). Plugging in the values, we get (-1 - (-5)) / (-9 - (-4)), which simplifies to 4 / -5. Therefore, the slope of the line is 4 / -5.

Rate this question:

• 10.

### State whether the slope is zero or undefined:

Explanation
The correct answer is zero. In mathematics, the slope of a line represents the steepness or incline of the line. A slope of zero indicates that the line is horizontal and has no incline. This means that the line is parallel to the x-axis and does not rise or fall as it extends. Therefore, the slope is zero.

Rate this question:

• 11.

### State whether the slope is zero or undefined:

Explanation
The slope is undefined when the line is vertical or parallel to the y-axis. In this case, the answer is "undefined" because it indicates that the slope cannot be determined or does not exist. The answer "Undefined" with a capital U may be a typographical error, but it still conveys the same meaning.

Rate this question:

• 12.

### State whether the slope is zero or undefined: (3, 4) and (-3, 4)

Explanation
The slope between two points is determined by the change in the y-coordinates divided by the change in the x-coordinates. In this case, the y-coordinates of both points are the same (4), while the x-coordinates have a difference of 6. Therefore, the change in y is 0, and the change in x is 6. Dividing 0 by 6 gives us a slope of 0. Hence, the slope between the two points is zero.

Rate this question:

• 13.

### State whether the slope is zero or undefined: (4, 3) and (4, -3)

Explanation
The slope between two points is calculated as the change in y-coordinates divided by the change in x-coordinates. In this case, the x-coordinates of the two points are the same (both 4), which means there is no change in the x-coordinate. Therefore, the change in x is 0. When dividing any number by 0, the result is undefined. Hence, the slope between these two points is undefined.

Rate this question:

• 14.

### Find the rate of change: The cost of group museum tickets is \$48 for four people (4, 48) and \$78 for ten people (10, 78).

Explanation
The rate of change can be found by calculating the difference in cost divided by the difference in number of people. In this case, the cost increased by \$30 (78 - 48) when the number of people increased by 6 (10 - 4). Therefore, the rate of change is \$30/6, which simplifies to \$5.

Rate this question:

• 15.

### Match the graph with the given information: (3, 5) slope: -2/1

A.
Explanation
The graph that matches the given information is a line that passes through the point (3, 5) and has a slope of -2/1. This means that for every increase of 1 unit in the x-coordinate, the y-coordinate decreases by 2 units. The line will have a negative slope, meaning it will slope downwards from left to right. The point (3, 5) will be on the line, and the line will continue in both directions.

Rate this question:

• 16.

C
c
• 17.

C
c
• 18.

A
a
• 19.

### Each pair of points lies on a line with the given slope. Find x. (2, 4) and (x, 8); slope = -2

x=0
x = 0
0
Explanation
The given information states that the two points (2, 4) and (x, 8) lie on a line with a slope of -2. To find the value of x, we can use the slope formula:

slope = (change in y) / (change in x)

Since the slope is -2, and the change in y is 8-4=4, we can substitute these values into the formula:

-2 = 4 / (x-2)

To solve for x, we can cross multiply:

-2(x-2) = 4

-2x + 4 = 4

-2x = 0

Dividing both sides by -2, we get:

x = 0

Therefore, the value of x is 0.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

• Current Version
• Apr 03, 2024
Quiz Edited by
ProProfs Editorial Team
• Dec 31, 2011
Quiz Created by