Question

Write an equation that gives the proportional relationship of the graph. A) y = 1 8 x B) y = 8x C) y = 9x D) y = 72x

Answer 1

For this case we must find a function of the form:

`y = mx + b`
Where,
m: slope of the line
b: cutting point with the y axis.
We note that the cutoff point with the y axis occurs at 0.
Therefore we have:

`b = 0`
On the other hand, the slope of the line is given by:

`m = (y2-y1)/(x2-x1)`
Substituting values we have:

`m = (72-0)/(9-0)`
Rewriting:

`m = (72)/(9)`

`m = 8`
Then, replacing values the equation of the line is:

`y=8x`
Answer:

`y=8x`
B) y = 8x

Answer 2

Here graph of an equation given.

The co-ordinates in the graph given are (0,0), (9,72), (18,144), (36,288), (45,360).

(0,0) point means, for x =0, y=0

(9,72) point means, for x =9, y=72

(18,144) means, for x =18, y=72

(36,288) means, for x = 36, y=288

(45,360) means, for x = 45, y =360.

We know that,
`(0)(8) = 0`,
`(9)(8) = 72`,
`(18)(8) = 144`,
`(36)(8) = 288`,
`(45)(8) = 360`,

That means in each point, y value is 8 times the x value.

That means, we can write the equation as
`y=8x` which also shows the proportional relationship of the graph.

So we have got the required answer.

The required equation is
`y=8x`.