The graph shows a line with constant of proportionality of 3/2 is option 4.
1. Constant of Proportionality:
Given the constant of proportionality is 3/2, this implies that for every 2 units of change in y (vertical movement), there will be a corresponding change of 3 units in x (horizontal movement). This can be represented by the ratio:
y / x = 3/2
2. Slope from Constant of Proportionality:
The slope (m) of a line can be calculated as the ratio of the change in y (Δy) to the change in x (Δx):
m = Δy / Δx
In this case, the ratio of y to x is already given by the constant of proportionality:
m = 3/2
Therefore, the line has a slope of m = 3/2.
3. Equation of the Line:
Since the line passes through the origin (0, 0), we can use the point-slope form of the linear equation:
y - y1 = m(x - x1)
where:
m is the slope (3/2)
(x1, y1) is the point of origin (0, 0)
Substituting the values, we get:
y - 0 = (3/2)(x - 0)
y = (3/2)x
Therefore, the equation of the line is y = (3/2)x.
Therefore, the answer is: The line would be a straight line passing through the origin with a slope of 3/2 which is graph 4.