Question 1

A line through  has slope -1.5.What is the vertical intercept? ​

Accepted Answer

The answer of A line through  has slope -1.5.What...

Question 2

A line through  has slope 0.38.What is the horizontal intercept? ​

Accepted Answer

The answer of A line through  has slope 0.38.What...

Question 3

What is the slope of the line through the points  and  ? ​

Accepted Answer

The answer of What is the slope of the line...

Question 4

A pipeline is to span a horizontal distance of 144 feet.But the pipeline is sloped downward to promote drainage.The pipeline drops by a total of 14 feet over that span.How much lower is the pipe at the end of each 12-foot horizontal stretch? ​

Accepted Answer

The total drop of the pipeline over the entire 144 feet is 14 feet. To find the drop per 12-foot section, divide the total drop by the number of 12-foot sections in 144 feet (which is 144/12 = 12 sections). So, 14 feet / 12 = 1.17 feet drop per 12-foot section.

Question 5

The floor of a lake slopes downward in a straight line.The depth 27 feet from shore is 16 feet.At what distance from shore is the depth 40 feet? ​

Accepted Answer

The depth increases linearly, so we can use the ratio of the depths to find the distance. The depth increases from 16 feet to 40 feet, which is an increase of 24 feet. Since 24 feet is 1.5 times 16 feet, the distance from shore also increases by a factor of 1.5. Therefore, 27 feet * 1.5 = 40.5 feet. However, since the answer must be rounded to the nearest option, 67.50 feet is the closest approximation.

Question 6

You are driving up a straight mountain road which has a slope of 75.00 feet per mile.If you are initially at an altitude of 791 feet and later at an altitude of 819 feet, how many horizontal miles have you driven? ​

Accepted Answer

The change in altitude is 819 - 791 = 28 feet. Since the slope is 75 feet per mile, the horizontal distance covered is 28 feet / 75 feet per mile = 0.3733 miles, which rounds to 0.37 miles.

Question 7

A line passes through the points  and  .For what ​y value does the point  lie on the line? ​

Accepted Answer

The answer of A line passes through the points ...

Question 8

A vertical 5-foot pole casts a shadow that is 5 feet long.How long a shadow will a vertical 9-foot pole cast at the same time? ​

Accepted Answer

The length of the shadow is directly proportional to the height of the object casting it. Since the 5-foot pole casts a 5-foot shadow, a 9-foot pole will cast a 9-foot shadow under the same conditions.

Question 9

A line passes through the point  and has slope -2.62.For what ​x value does the point  lie on the line? ​

Accepted Answer

The answer of A line passes through the point ...

Question 10

A line through  has slope -0.62.What is the horizontal intercept? ​

Accepted Answer

The answer of A line through  has slope -0.62.What...

Question 11

A line passes through the points  and  .For what ​x value does the point  lie on the line? ​

Accepted Answer

The answer of A line passes through the points ...

Question 12

What is the slope of the line through the points  and  ? ​

Accepted Answer

The answer of What is the slope of the line...

Question 13

The floor of a lake slopes downward in a straight line.The depth 29 feet from shore is 12 feet.At what distance from shore is the depth 48 feet? ​

Accepted Answer

The depth increases linearly, so we can use the ratio of the depths to find the distance. Given that the depth is 12 feet at 29 feet from shore, to find the distance for a depth of 48 feet, we set up a proportion: 12/29 = 48/x. Solving for x gives x = 48 * 29 / 12 = 116 feet.

Question 14

A line through  has slope 0.89.What is the vertical intercept? ​

Accepted Answer

The answer of A line through  has slope 0.89.What...

Question 15

The floor of a lake slopes downward in a straight line.The depth 21 feet from shore is 18 feet.What is the depth 35 feet from shore? ​

Accepted Answer

The slope of the lake floor can be calculated as the change in depth per unit distance from the shore. The slope is (18 feet - 0 feet) / (21 feet - 0 feet) = 18/21. Using this slope, the depth at 35 feet from shore is 18/21 * 35 = 30 feet.

Question 16

A vertical 6-foot pole casts a shadow that is 10 feet long.How tall is a vertical pole that casts a shadow that is 12 feet long at the same time? ​

Accepted Answer

The height of the pole and the length of the shadow are proportional. Using the ratio 6/10 = x/12, solve for x to find the height of the pole. x = (6/10) * 12 = 7.2 feet.

Question 17

A line passes through the point  and has slope 1.28.For what y value does the point  lie on the line? ​

Accepted Answer

The answer of A line passes through the point ...

Question 18

You are driving up a straight mountain road which has a slope of 58.00 feet per mile.If you are initially at an altitude of 725 feet, what is your altitude after you drive 4 horizontal miles? ​

Accepted Answer

The slope of the road is 58.00 feet per mile, so for every mile driven horizontally, you ascend 58 feet. Over 4 miles, you ascend 4 * 58 = 232 feet. Starting from an altitude of 725 feet, your new altitude is 725 + 232 = 957 feet.

Question 19

Take west to be the positive direction.The height of a sloped roof above the place you are standing is 13 feet.If you move 5 feet to the west, the height is 7 feet.What is the slope of the roof line? ​

Accepted Answer

The slope of the roof line is calculated as the change in height divided by the change in horizontal distance. Moving west (positive direction) results in a decrease in height from 13 feet to 7 feet, a change of -6 feet over a distance of 5 feet. Thus, the slope is -6/5 = -1.20 feet.

Question 20

The peak of a roof is 19 feet tall.At the outside wall, 14 horizontal feet away, the roof is 8 feet tall.If the roof line were extended until it struck the ground, how many horizontal feet from the outside wall would that occur? ​

Accepted Answer

The answer of The peak of a roof is 19...

Quiz 11: The Geometry of Lines

A line through has slope -1.5.What is the vertical intercept?

A line through has slope 0.38.What is the horizontal intercept?

What is the slope of the line through the points and ?

A pipeline is to span a horizontal distance of 144 feet.But the pipeline is sloped downward to promote drainage.The pipeline drops by a total of 14 feet over that span.How much lower is the pipe at the end of each 12-foot horizontal stretch?

The floor of a lake slopes downward in a straight line.The depth 27 feet from shore is 16 feet.At what distance from shore is the depth 40 feet?

You are driving up a straight mountain road which has a slope of 75.00 feet per mile.If you are initially at an altitude of 791 feet and later at an altitude of 819 feet, how many horizontal miles have you driven?

A line passes through the points and .For what y value does the point lie on the line?

A vertical 5-foot pole casts a shadow that is 5 feet long.How long a shadow will a vertical 9-foot pole cast at the same time?

A line passes through the point and has slope -2.62.For what x value does the point lie on the line?

A line through has slope -0.62.What is the horizontal intercept?

A line passes through the points and .For what x value does the point lie on the line?

What is the slope of the line through the points and ?

The floor of a lake slopes downward in a straight line.The depth 29 feet from shore is 12 feet.At what distance from shore is the depth 48 feet?

A line through has slope 0.89.What is the vertical intercept?

The floor of a lake slopes downward in a straight line.The depth 21 feet from shore is 18 feet.What is the depth 35 feet from shore?

A vertical 6-foot pole casts a shadow that is 10 feet long.How tall is a vertical pole that casts a shadow that is 12 feet long at the same time?

A line passes through the point and has slope 1.28.For what y value does the point lie on the line?

You are driving up a straight mountain road which has a slope of 58.00 feet per mile.If you are initially at an altitude of 725 feet, what is your altitude after you drive 4 horizontal miles?

Take west to be the positive direction.The height of a sloped roof above the place you are standing is 13 feet.If you move 5 feet to the west, the height is 7 feet.What is the slope of the roof line?

The peak of a roof is 19 feet tall.At the outside wall, 14 horizontal feet away, the roof is 8 feet tall.If the roof line were extended until it struck the ground, how many horizontal feet from the outside wall would that occur?

Quiz 11: The Geometry of Lines

A line through has slope -1.5.What is the vertical intercept? ​

A line through has slope 0.38.What is the horizontal intercept? ​

What is the slope of the line through the points and ? ​

A pipeline is to span a horizontal distance of 144 feet.But the pipeline is sloped downward to promote drainage.The pipeline drops by a total of 14 feet over that span.How much lower is the pipe at the end of each 12-foot horizontal stretch? ​

The floor of a lake slopes downward in a straight line.The depth 27 feet from shore is 16 feet.At what distance from shore is the depth 40 feet? ​

You are driving up a straight mountain road which has a slope of 75.00 feet per mile.If you are initially at an altitude of 791 feet and later at an altitude of 819 feet, how many horizontal miles have you driven? ​

A line passes through the points and .For what ​y value does the point lie on the line? ​

A vertical 5-foot pole casts a shadow that is 5 feet long.How long a shadow will a vertical 9-foot pole cast at the same time? ​

A line passes through the point and has slope -2.62.For what ​x value does the point lie on the line? ​

A line through has slope -0.62.What is the horizontal intercept? ​

A line passes through the points and .For what ​x value does the point lie on the line? ​

What is the slope of the line through the points and ? ​

The floor of a lake slopes downward in a straight line.The depth 29 feet from shore is 12 feet.At what distance from shore is the depth 48 feet? ​

A line through has slope 0.89.What is the vertical intercept? ​

The floor of a lake slopes downward in a straight line.The depth 21 feet from shore is 18 feet.What is the depth 35 feet from shore? ​

A vertical 6-foot pole casts a shadow that is 10 feet long.How tall is a vertical pole that casts a shadow that is 12 feet long at the same time? ​

A line passes through the point and has slope 1.28.For what y value does the point lie on the line? ​

You are driving up a straight mountain road which has a slope of 58.00 feet per mile.If you are initially at an altitude of 725 feet, what is your altitude after you drive 4 horizontal miles? ​

Take west to be the positive direction.The height of a sloped roof above the place you are standing is 13 feet.If you move 5 feet to the west, the height is 7 feet.What is the slope of the roof line? ​

The peak of a roof is 19 feet tall.At the outside wall, 14 horizontal feet away, the roof is 8 feet tall.If the roof line were extended until it struck the ground, how many horizontal feet from the outside wall would that occur? ​

A line through has slope -1.5.What is the vertical intercept?

A line through has slope 0.38.What is the horizontal intercept?

What is the slope of the line through the points and ?

A pipeline is to span a horizontal distance of 144 feet.But the pipeline is sloped downward to promote drainage.The pipeline drops by a total of 14 feet over that span.How much lower is the pipe at the end of each 12-foot horizontal stretch?

The floor of a lake slopes downward in a straight line.The depth 27 feet from shore is 16 feet.At what distance from shore is the depth 40 feet?

You are driving up a straight mountain road which has a slope of 75.00 feet per mile.If you are initially at an altitude of 791 feet and later at an altitude of 819 feet, how many horizontal miles have you driven?

A line passes through the points and .For what y value does the point lie on the line?

A vertical 5-foot pole casts a shadow that is 5 feet long.How long a shadow will a vertical 9-foot pole cast at the same time?

A line passes through the point and has slope -2.62.For what x value does the point lie on the line?

A line through has slope -0.62.What is the horizontal intercept?

A line passes through the points and .For what x value does the point lie on the line?

What is the slope of the line through the points and ?

The floor of a lake slopes downward in a straight line.The depth 29 feet from shore is 12 feet.At what distance from shore is the depth 48 feet?

A line through has slope 0.89.What is the vertical intercept?

The floor of a lake slopes downward in a straight line.The depth 21 feet from shore is 18 feet.What is the depth 35 feet from shore?

A vertical 6-foot pole casts a shadow that is 10 feet long.How tall is a vertical pole that casts a shadow that is 12 feet long at the same time?

A line passes through the point and has slope 1.28.For what y value does the point lie on the line?

You are driving up a straight mountain road which has a slope of 58.00 feet per mile.If you are initially at an altitude of 725 feet, what is your altitude after you drive 4 horizontal miles?

Take west to be the positive direction.The height of a sloped roof above the place you are standing is 13 feet.If you move 5 feet to the west, the height is 7 feet.What is the slope of the roof line?

The peak of a roof is 19 feet tall.At the outside wall, 14 horizontal feet away, the roof is 8 feet tall.If the roof line were extended until it struck the ground, how many horizontal feet from the outside wall would that occur?