To derive the equation of a line in the form y = mx through the origin, we need to determine the value of the slope, m. In a proportional relationship, the slope represents the constant rate of change.
Looking at the graph of the proportional relationship, we can observe that as the x-values increase, the y-values also increase proportionally. This suggests that the slope should be positive.
Since the line passes through the origin (0, 0), we can use any two points on the line to calculate the slope.
Let's choose two points on the line:
Point A: (1, 2)
Point B: (2, 4)
The slope, m, can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the values from the points A and B:
m = (4 - 2) / (2 - 1)
m = 2 / 1
m = 2
Thus, the slope of the line y = mx through the origin is 2.
The equation of the line can be written as:
y = 2x
The proportional relationship is shown on the graph.Derive the equation of the line y=mx through the origin
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