Multiple Choice

Find the slope.

A coordinate graph shows a line through 2 points. One point has coordinates negative 3 comma 3. The other point has coordinates 1 comma negative 5.
A. 2
B. –one-half
C. –2
D. one-half

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Using the coordinates given, we have:

x1 = -3, y1 = 3
x2 = 1, y2 = -5

slope = (-5 - 3) / (1 - (-3)) = (-8) / 4 = -2

Therefore, the answer is (C) –2.

Use the graph below to answer the following question.

Find the slope of the line. Describe how one variable changes in relation to the other.
A coordinate graph is titled Distance Traveled. The horizontal axis is titled Time in hours. The vertical axis is titled Distance in miles.

The line starts at the origin and passes through the point with coordinates 1 comma 2, the point with coordinates 2 comma 4, the point with coordinates 3 comma 6, and the point with coordinates 4 comma 8.
A. 2; distance increases by 2 miles per hour
B. 2; distance decreases by 2 miles per hour
C. one-half; distance increases 1 mile every 2 hours
D. one-half; distance decreases 1 mile every 2 hours

The slope of the line can be found by selecting any two points on the line and using the formula:

slope = (change in distance) / (change in time)

Let's use the points (1, 2) and (4, 8) to calculate the slope:

slope = (8 - 2) / (4 - 1) = 6 / 3 = 2

Therefore, the answer is (A) 2.

The slope of 2 means that for every hour of time, the distance traveled increases by 2 miles. This can be seen by following the line on the graph - it is a straight line that goes up and to the right, indicating a constant increase in distance with respect to time.

Use the graph below to answer the following question.

Find the slope of the line. Describe how one variable changes in relation to the other.
a line is graphed on a coordinate grid.

The title of the graph is Draining Tub. The horizontal axis is titled time in minutes. The vertical axis is titled Water in gallons.
A line is graphed starting at the point with coordinates 0 comma 14, then passing through the point with coordinates 3 comma 12, the point with coordinates 6 comma 10, the point with coordinates 9 comma 8, the point with coordinates 12 comma 6, and the point with coordinates 15 comma 4.
A. start fraction 2 over 3 end fraction; the amount of water decreases by 2 gallons every 3 minutes.
B. negative two-thirds; the amount of water decreases by 2 gallons every 3 minutes.
C. negative three-halves; the amount of water decreases by 3 gallons every 2 minutes.
D. –1 ; the amount of water decreases by 1 gallon per minute.
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2 of 8 Answered

The slope of the line can be found by selecting any two points on the line and using the formula:

slope = (change in water) / (change in time)

Let's use the points (0, 14) and (3, 12) to calculate the slope:

slope = (12 - 14) / (3 - 0) = -2 / 3

Therefore, the answer is (B) negative two-thirds.

The negative slope means that as time increases (in minutes), the amount of water in the tub decreases. Specifically, the amount of water decreases by 2 gallons for every 3 minutes that pass. This can be seen by following the line on the graph - it is a straight line that goes down and to the right, indicating a constant decrease in water with respect to time.

The data in the table are linear. Use the table to find the slope.

x

2

4

6

8

y

1

-2

-5

-8

A. The fraction states 3 over 4.
B. negative three-halves
C. negative two-thirds
D. two-thirds

The slope of a linear relationship between two variables x and y can be found using the formula:

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

We can select any two points from the table and use them to calculate the slope. Let's use the first and last points:

slope = (y2 - y1) / (x2 - x1) = (-8 - 1) / (8 - 2) = -9 / 6

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3:

slope = (-9 / 3) / (6 / 3) = -3 / 2

Therefore, the answer is (B) negative three-halves.

Graph the linear function in questions 5 and 6.

y equals one third x minus 4
A. A line is graphed on the coordinate plane. The line passes through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis 5 comma 3 right-parenthesis.
B. A line is graphed on the coordinate plane. The line passes through the points left-parenthesis 0 comma negative 4 right-parenthesis and left-parenthesis 2 comma 2 right-parenthesis.
C. A line is graphed on the coordinate plane. The line passes through the points left-parenthesis negative 3 comma negative 5 right-parenthesis and left-parenthesis 0 comma negative 4 right-parenthesis.
D. A line is graphed on the coordinate plane. The line passes through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 2 comma 3 right-parenthesis.
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4 of 8 Answered

To graph the linear function y = (1/3)x - 4, we can plot two points and draw a straight line through them. One way to do this is to choose x values and use the equation to find the corresponding y values. For example:

When x = 0:
y = (1/3)(0) - 4 = -4
So one point is (0, -4).

When x = 3:
y = (1/3)(3) - 4 = -3
So another point is (3, -3).

Plotting these two points and drawing a straight line through them gives us:

```
|
3 +--------------
| /
| /
| /
0 +--------------
|
-4

|---|---|---|--
0 3 6 x
```

Therefore, the answer is (A) A line is graphed on the coordinate plane. The line passes through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis 5 comma 3 right-parenthesis.

y = –2x + 3

A. linear function of graph
B. linear function of graph
C. linear function of graph
D. linear function of graph
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5 of 8 Answered