Question

the graph shows proportional relationship between the variables y and x. write an equation to model the relationship.use pencil and paper . explain how you know there is a proportional relationship if you este given either an equation or a graph

Answer 1

y = 11x

Explanation:

I know there is a proportional relationship because the line is straight and passes the Origin (graph) or has the same unit rate (table).

Answer 2

This equation confirms that there is a proportional relationship between the variables y and x, with a constant of proportionality of 5/2.

To find the equation that models this relationship, we can use the slope-intercept form of a linear equation:

y = mx + b

where:

m is the slope of the line

b is the y-intercept (the point where the line crosses the y-axis)

In a proportional relationship, the slope is equal to the constant of proportionality. We can find the slope by picking two points on the line and using the formula:

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

From the graph, you can choose any two points that fall on the line. For example, you could use the points (4, 10) and (10, 25). Substituting these values into the formula, we get:

m = (25 - 10) / (10 - 4) = 15 / 6 = 5/2

Therefore, the equation that models the relationship is:

y = (5/2)x + b

We can find the y-intercept (b) by setting x to 0 and solving for y. In this case, y = (5/2) * 0 + b = 0 + b = b. Since the line passes through the origin, we know that b must be 0.

Therefore, the final equation that models the relationship is:

y = (5/2)x