Question

Find the equation that represents the proportional relationship in this graph,

for y in terms of a.
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
C
0.1
3
O
0.2
0.4
0.6
0.8

Answer 1

An equation that represents the proportional relationship in this graph, for y in terms of x is y = 0.75x.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

• y represents the y-variable​.
• x represents the x-variable.
• k is the constant of proportionality.

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 0.3/0.4

Constant of proportionality, k = 0.75.

Therefore, the required linear equation that represents the proportional relationship in this graph is given by;

y = kx

y = 0.75x

Answer 2

Explanation:

the best is always to look for points on the line that are exactly corner points of grid squares.

I find e.g.

(0.3, 0.4) and (0.6, 0.8)

so, the linear equation is

y = ax + b

0.4 = a×0.3 + b

0.8 = a×0.6 + b

let's subtract the second from the first equation :

-0.4 = a×-0.3 + 0

a = -0.4/-0.3 = 0.4/0.3 = 4/3

so, the equation is

y = (4/3)x