To derive the equation of the line y=mx through the origin, we need the value of the slope, m.
In a proportional relationship, the ratio of y to x is constant. This means that for every value of x, the corresponding value of y is equal to the constant ratio multiplied by x.
If we have two points (x1, y1) and (x2, y2) on the line, the ratio of y to x will be the same for any pair of points on the line. Therefore, we can choose any two points to calculate the slope.
Since the line passes through the origin (0, 0), one point is already given. Let's choose another point on the line: (x, y).
According to the proportional relationship, the ratio of y to x is the same for any pair of points on the line. So we have:
(y1/x1) = (y/x)
Since we are looking for the equation of the line, we can rewrite this ratio as:
y/x = m
where m is the slope of the line.
Therefore, the equation of the line y=mx through the origin is:
y = mx
The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.
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1 answer