Question

Decide which of the following equations represents a proportional relationship.

A) y = 3x + 1
B) y = x + 1
C) y = 1/3x
D) y = x/3 - 3

Answer 1

[AI-generated answer — Bot GPT 3.5]

C) y = 1/3x

Answer 2

on a graph, there is a line with points being: (1, - 1), (0, -4)

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

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to calculate the slope of the line using the given points.

The formula for calculating the slope between two points (x1, y1) and (x2, y2) is:

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

Given points are (1, -1) and (0, -4), we can substitute these values into the slope formula:

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

Now that we have calculated the slope, we can use the slope-intercept form of a linear equation, which is: y = mx + b. We can plug in the calculated slope (m = 3) and one of the points (0, -4) into the equation to solve for the y-intercept (b).

Using the point (0, -4):
-4 = 3(0) + b
-4 = b

Now we have the slope (m = 3) and the y-intercept (b = -4). We can write our equation of the line in slope-intercept form:
y = 3x - 4

Therefore, the equation of the line in slope-intercept form is y = 3x - 4.

Answer 4

on a graph, there is a line with points being: (0, 1), (1, -4)

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

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to calculate the slope of the line using the two given points.

The formula for calculating the slope between two points (x1, y1) and (x2, y2) is:

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

Given points are (0, 1) and (1, -4), we can substitute these values into the slope formula:

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

Now that we have calculated the slope, we can use the slope-intercept form of a linear equation, which is y = mx + b. We can plug in the calculated slope (m = -5) and one of the points (0, 1) into the equation to solve for the y-intercept (b).

Using the point (0, 1):
1 = -5(0) + b
1 = b

Now we have the slope (m = -5) and the y-intercept (b = 1). We can write our equation of the line in slope-intercept form:
y = -5x + 1

Therefore, the equation of the line in slope-intercept form is y = -5x + 1.

Answer 6

on a graph, there is a line with points being: (0, 3), (3, 2)

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

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to calculate the slope of the line using the two given points.

The formula for calculating the slope between two points (x1, y1) and (x2, y2) is:

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

Given points are (0, 3) and (3, 2), we can substitute these values into the slope formula:

m = (2 - 3) / (3 - 0)
m = (-1) / 3
m = -1/3

Now that we have calculated the slope, we can use the slope-intercept form of a linear equation, which is y = mx + b. We can plug in the calculated slope (m = -1/3) and one of the points (0, 3) into the equation to solve for the y-intercept (b).

Using the point (0, 3):
3 = -1/3 * 0 + b
3 = b

Now we have the slope (m = -1/3) and the y-intercept (b = 3). We can write our equation of the line in slope-intercept form:
y = -1/3 x + 3

Therefore, the equation of the line in slope-intercept form is y = -1/3 x + 3.