Question

The graph shows the proportional relationship. Derive the equation of the line y = mx through the origin.
With the coordinates A (1,5) and B (2,10).(1 point)
Answer
Use the graph to derive the equation of the line in slope-intercept form. With the coordinates A (0,-2) and B (1,3)
(1 point)
Answer
Identify the slope and y-intercept of the line. Provide the most simplified form of the slope. With the coordinates A (0,6) and B (-2,2)
(1 point)
The slope is ? . The y-intercept is (0,?).
Answer
Interpret the slope in the context of this situation. Give the most simplified rate using whole numbers. With the coordinates A (0,5) and B (5,8).
(1 point)

Someone had 5 weeks to read a book.

• Someone reads 3 books every 5 weeks.

•Someone is reading 5 books every 3 weeks.

• Someone read 5 books in a week.
Answer
For a 5th grader, describe what makes a proportion. Give an example of a proportion. (2 points)
Answered by GPT 3.5
First, determine the slope (m) of the line passing through points A and B using the formula:

m = (y2 - y1) / (x2 - x1)
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5

Next, substitute the slope (m) into the equation of a line y = mx through the origin:

y = 5x

Therefore, the equation of the line passing through the origin and points A and B is y = 5x.
Answered by GPT 3.5
First, determine the slope (m) of the line passing through points A and B using the formula:

m = (y2 - y1) / (x2 - x1)
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5

Next, substitute the slope (m) and one of the points (A or B) into the slope-intercept form of a line y = mx + b to solve for the y-intercept (b):

Using point A (0, -2):
-2 = 5(0) + b
-2 = 0 + b
b = -2

Therefore, the equation of the line passing through points A and B in slope-intercept form is y = 5x - 2.
Answered by GPT 3.5
First, determine the slope (m) of the line passing through points A (0,6) and B (-2,2) using the formula:

m = (y2 - y1) / (x2 - x1)
m = (2 - 6) / (-2 - 0)
m = -4 / -2
m = 2

So, the slope of the line is 2.

To find the y-intercept, we can use the slope-intercept form of a line y = mx + b and substitute one of the points given. Let's use point A (0,6):

6 = 2(0) + b
6 = b

So, the y-intercept is (0,6).
Answered by GPT 3.5
The slope of the line passing through points A (0,5) and B (5,8) is calculated as follows:

m = (y2 - y1) / (x2 - x1)
m = (8 - 5) / (5 - 0)
m = 3 / 5

The simplified rate using whole numbers is 3 books every 5 weeks.

Interpreting the slope in this context: The slope of 3 books every 5 weeks implies that for each additional week, the individual reads an average of 3 more books. This rate represents the linear relationship between the number of weeks and the number of books read.
Answered by GPT 3.5
In simple terms, a proportion is a relationship between two ratios that are equal to each other. It is a comparison of two quantities in the form of fractions, where the two ratios have the same value.

For example, let's consider the proportion:

3/5 = 6/10

This proportion states that the ratio of 3 to 5 is equal to the ratio of 6 to 10. It shows that the two fractions have the same value, making it a proportion. In this example, both sides of the proportion can be simplified to 3/5, demonstrating the equality of the ratios. Understanding proportions is important in math as they are used in various real-life situations to compare different quantities or solve problems involving ratios.