The graph of a proportional relationship will always be a straight line that passes through the origin. Why?

Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.

If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.

As the coordinates of the origin are always (0,0), the graph  (Or the slope) would surely pass through the origin.

Example :

If we consider a graph such that x=y.

And if we multiply or divide any real number (a) between them.

ax=ay

As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

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step-by-step explanation: