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

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 $y=8x$.

Answer 2

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:
 $m = \frac{y2-y1}{x2-x1}$
 Substituting values we have:
 $m = \frac{72-0}{9-0}$
 Rewriting:
 $m = \frac{72}{9}$
 $m = 8$
 Then, replacing values the equation of the line is:
 $y=8x$
 Answer:
 $y=8x$
 B) y = 8x