Question

The graph shows a relationship between two quantities.ДУ200018001600140012001000800600400200ХOd-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables?

Answer 1

The most accurate representation of the relationship between the variables in the graph is y = 150+1500x.

First, determine the slope.

Choose any two points and find their coordinates

(0, 1500) and (2, 1800)

x₁ = 0 y₁=1500 x₂=2 y₂=1800

Substitute the values into the formula below to find the slope

The y-intercept(b) of the graph is b=1500

Substitute the values of the slope and intercept into y=mx +b

This gives the equation of the graph is y = 150+1500x

Here's why the other options are not as accurate:

A. y = 150 + 1500x: This equation would result in a graph with a similar slope but a different y-intercept. The actual graph seems to pass through the origin (0, 0), while this equation would have a y-intercept of 150.

B. y = 100 - 15: This equation would result in a horizontal line with a y-intercept of 100, which is not consistent with the upward slope of the graph.

C. y = 15 - 100г: This equation appears to be unrelated to the graph and includes an unknown symbol "г".

Therefore, based on the visual evidence, y = 150+1500x is the most accurate representation of the relationship between the variables in the graph.

Complete question:

Which equation best represents the relationship between the variables?

A. y = 150+1500x

B. y = 100 - 15

C. y=15- 100г

D. Y = 1500+150x

Answer 2

First let't find the slope

Pick any two point and locate its coordinate

(0, 1500) and (2, 1800)

x₁ = 0 y₁=1500 x₂=2 y₂=1800

substitute the values into the formula below to find the slope

`\text{slope(m)}=(y_2-y_1)/(x_2-x_1)`

`=(1800-1500)/(2-0)`
`=(300)/(2)=150`

The y-intercept(b) of the graph is b=1500

Substitute the values of the slope and intercept into y=mx +b

This gives the equation of the graph.

That is:

`y=150x\text{ + 1500}`