Graph the line that represents a proportional relationship between yyy and xxx where the unit rate of change of yyy with respect to xxx is \,\dfrac{4}{3} 3 4 start fraction, 4, divided by, 3, end fraction . In other words, a change of 111 unit in xxx corresponds to a change of \,\dfrac{4}{3} 3 4 start fraction, 4, divided by, 3, end fraction units in yyy. Graph the line and write the equation of the line. The equation is .

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m or unit rate of the line and the line passes through the origin

so

In this problem we have

[tex]k=\frac{4}{3}[/tex]

substitute

[tex]y=\frac{4}{3}x[/tex]

using a graphing tool

The graph in the attached figure

abidemiokin abidemiokin · Answer 2 · 2021-10-02T01:24:50+02:00

The required equation of the line will be expressed as [tex]y = \frac{4}{3} x[/tex]

If the variable y is directly proportional to x, this is expressed as:

[tex]y \alpha x\\[/tex]

Introducing the proportionality constant will give [tex]y = kx\\[/tex] where k is the constant of proportionality.

If the unit constant "k" given is 4/3, the required equation of the line will be expressed as [tex]y = \frac{4}{3} x[/tex]

Plotting the graph of the equation. Note that:

The y-intercept of the line is zero
The line will pass through the origin (0, 0)

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