2. Use the graph the answer the following questions.

Question

The graph basically shows an arrow going straight up and an arrow on the same arrow going up but its down the arrow going up is called "y-axis" and the arrow on the bottom of the same arrow going up on it is called "x-axis" and there is on y axis on the top of the line the number 70 and then below 70 is 60 then 50 then 40 then 30 then 20 then 10 and on x-axis there is -1, then 0, then 1, then 2, then 3, then 4, then 5, then 6, then 7, then lastly 8 and from the c-axis arrow there is an arrow going Diagonally up from the 0 on x-axis all the way to a little bit above the 70 on y-axis and at the bottom of x-axis it says "Time (in hours)

a. The constant of proportionality is
.

b. Write an equation that represents this graph
.

c. This is a proportional relationship because the y-intercept is

1, 30, 0, 15, y = x - 15, y = 15x, y = x + 15, y = 3/2x, (2, 30), (0, 15), (0, 0)

Answer 1

To answer your questions based on the provided description of the graph, we will follow standard methods for identifying characteristics in a linear graph.

a. The constant of proportionality is

In a linear equation of the form \( y = mx + b \), the constant of proportionality is represented by \( m \), the slope. The slope can be calculated by selecting points on the graph. From your description, the line goes through at least one point (0, 0), which implies that the relationship is proportional.

From the description, if we assume one of the points is (0, 15) and another is (4, 70), we can calculate the slope or constant of proportionality \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{70 - 15}{4 - 0} = \frac{55}{4} = 13.75 \]

However, if the line does pass through (0, 0) based on the proportional relationship, then we would use that point. But since (0, 15) is mentioned, let's proceed with that for now.

b. Write an equation that represents this graph

From your descriptions of points, specifically if we have (0, 15) as the y-intercept and you want to calculate a slope based on another point like (4, 70):

First, the form of the equation through a point with slope:

• Start with \( y - y_1 = m(x - x_1) \)

We could reformulate to find \( y = mx + b \):

Given:

1. Slope \( m = \frac{55}{4} \)
2. Point (0, 15) gives us \( b = 15\)

So:

\[ y = 13.75x + 15 \quad \text{(if the line goes through (0, 15) as stated)} \]

However, if we are confirming values at (0, 0) for a true proportional relationship, then the correct equation will be:

\[ y = \frac{55}{4}x \quad \text{(since b = 0)} \]

c. This is a proportional relationship because the y-intercept is

For a relationship to be proportional, the y-intercept must be 0. Based on the choices given:

• (0, 0) suggests proportion.
• (0, 15) would not imply proportionality because the y-intercept is not zero.

Therefore, the response should be:

This is a proportional relationship because the y-intercept is (0, 0).

If you have further specificity regarding the values or a more accurate point for the slope calculation or the positioning of the line in question, please provide that info for more tailored responses!