Question

Using the graph, derive the equation of the line in slope-intercept form.

Answer Choices:
* y = 3x + 4
* y = −3x − 4
* 3x − y = 4
* y = 3x − 4

The coordinates are (0, -4), (1, -1)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to find the slope (m) of the line. The slope is given by the formula:

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

Using the coordinates (0, -4) and (1, -1) given in the graph:

m = (-1 - (-4)) / (1 - 0)
m = (3) / (1)
m = 3

Next, we can use the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept. Now we need to find the y-intercept. Given that the point (0, -4) lies on the line, we can substitute these values into the equation to find b:

-4 = 3(0) + b
-4 = b

Therefore, the equation of the line in slope-intercept form is:

y = 3x - 4

Therefore, the correct answer choice is: y = 3x - 4

Answer 2

Question:

Write the equation of the line in slope-intercept form.

Answer Choices:
* y = 5x + 1
* y = −5x + 1
* −5x − y = −1
* y = −5x − 1

The coordinates are (0, 1), (1, -4)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to find the slope (m) of the line. The slope is given by the formula:

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

Using the coordinates (0, 1) and (1, -4) given in the question:

m = (-4 - 1) / (1 - 0)
m = (-5) / (1)
m = -5

Next, we can use the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept. Now we need to find the y-intercept. Given that the point (0, 1) lies on the line, we can substitute these values into the equation to find b:

1 = -5(0) + b
1 = b

Therefore, the equation of the line in slope-intercept form is:

y = -5x + 1

Therefore, the correct answer choice is: y = -5x + 1

Answer 4

Question:

Use the table to answer the question.
x y
−2 −1
0 1
2 3

Write an equation that represents this non-proportional linear relationship.

Answer Choices:
* y = x + 1
* y = 1/2x + 1
* y= −2x + 1
* y = x + 2

Answer 5

[AI-generated answer — Bot GPT 3.5]

To write an equation that represents the relationship between x and y for the given values in the table, we need to find the slope (m) and the y-intercept (b) for the non-proportional linear relationship.

First, we find the slope using two points from the table. Let's use the points (0, 1) and (2, 3):

m = (y2 - y1) / (x2 - x1)
m = (3 - 1) / (2 - 0)
m = 2 / 2
m = 1

Now that we have the slope, we can find the y-intercept by substituting one of the given points into the equation y = mx + b. Let's use the point (0, 1):

1 = 1(0) + b
b = 1

Therefore, the equation that represents the non-proportional linear relationship is:

y = x + 1

Therefore, the correct answer choice is: y = x + 1

Answer 6

Question:

A family is going from Dallas, Texas, to Los Angeles, California. They have traveled 500 miles so far. The next day, their average speed is 70 miles per hour. Write an equation for the distance they traveled, y, and the hours they have driven, x. Indicate whether this is a proportional or a non-proportional situation.

Answer Choices:
* y = 500x + 70, non-proportional
* y = 70x + 500, proportional
* y = 70x + 500, non-proportional
* y = 70x, proportional

Answer 7

[AI-generated answer — Bot GPT 3.5]

In this scenario, the family has already traveled 500 miles, which is the initial distance. The distance they travel on the next day can be represented as the product of the speed (70 miles per hour) and the time they drive. Therefore, the equation for the distance they traveled (y) in terms of the hours they have driven (x) can be written as:

y = 70x + 500

This equation is non-proportional because there is an initial 500-mile distance component that is constant, regardless of the time driven. The total distance traveled depends on two factors: the constant initial distance (500 miles) and the distance traveled based on the speed (70 miles per hour) and time driven (x hours).

Therefore, the correct answer choice is: y = 70x + 500, non-proportional

Answer 8

You are baking a cake. For every three cups of flour, you need to add two eggs. Write an equation for the relationship between the number of eggs, y, and the amount of flour, x. Distinguish whether this is a proportional or non-proportional situation.

Answer Choices:
* y = 32x, proportional.
* y = 23x, proportional.
* y = 3x + 2, non-proportional.
* y = 2x + 3, non-proportional.

Answer 9

[AI-generated answer — Bot GPT 3.5]

In this scenario, the relationship between the number of eggs (y) and the amount of flour (x) is not directly proportional. Instead, for every three cups of flour, you need to add two eggs. This means that for each unit of change in the amount of flour, the number of eggs will not change by a constant factor.

The equation representing the relationship between the number of eggs (y) and the amount of flour (x) can be written as:
y = (2/3)x

This equation reflects the fact that two eggs are added for every three cups of flour. It is not directly proportional because the ratio of eggs to flour is not constant.

Therefore, the correct answer is not among the provided choices. The correct relationship is:
y = (2/3)x