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

For this case we must find a function of the form:
[tex]y = mx + b [/tex]
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:
[tex] b = 0 [/tex]
On the other hand, the slope of the line is given by:
[tex]m = \frac{y2-y1}{x2-x1} [/tex]
Substituting values we have:
[tex]m = \frac{72-0}{9-0} [/tex]
Rewriting:
[tex]m = \frac{72}{9} [/tex]
[tex]m = 8 [/tex]
Then, replacing values the equation of the line is:
[tex]y=8x[/tex]
Answer:
[tex]y=8x[/tex]
B) y = 8x

eurydike eurydike · Answer 2 · 2018-08-22T10:45:53+02:00

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, [tex] (0)(8) = 0 [/tex], [tex] (9)(8) = 72 [/tex], [tex] (18)(8) = 144 [/tex], [tex] (36)(8) = 288 [/tex], [tex] (45)(8) = 360 [/tex],

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

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

So we have got the required answer.

The required equation is [tex] y=8x [/tex].